Algebra › Quadratic equations

Completing the square

Solve the first problem 18 problems

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1. Completing the square parameter ●○○○○ 10 ptsThe equation $x^2 + 2x - 2 = 0$ is transformed into the form $(x + m)^2 = 3$ by completing the square. Find the value of $m$.
2. Solve a quadratic with square roots ●○○○○ 10 ptsSolve $0=2x^2-18$ for $x$. Give both solutions.
3. Solve a shifted square equation ●○○○○ 10 ptsSolve $(x-4)^2-9=0$ for $x$. Give both solutions.
4. Quadratic equation in two variables ●●○○○ 20 ptsSolve the equation $x^{2}-2x+y^{2}-4y+5=0$ for real numbers $x$ and $y$. Find $x$ and $y$.
5. Completing the square for a quartic ●●○○○ 20 ptsRewrite the expression $g^4 + 12g^2 + 9$ in the form $c(g^2 + p)^2 + q$. What is $q$?
6. Roots by completing the square ●●○○○ 20 ptsFind the roots of $2x^2 - 7x + 3 = 0$ by completing the square.

More in Quadratic equations

Conditions on the rootsEquations reducible to quadraticsExpressions in the rootsInteger roots with a parameterMinimum of a quadraticPrime roots of quadraticsQuadratic bounds on an intervalQuadratic formulaQuadratics with integer coefficientsSolving by factoringSums and products of solutionsZeros of a quadratic function