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Simplifying 4x2 + -6x = 22 Reorder the terms: -6x + 4x2 = 22 Solving -6x + 4x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + -6x + 4x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + -3x + 2x2 = 0 Solving -11 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -1.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -1.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -1.5x + x2 = 0 + 5.5 -1.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -1.5x + x2 = 5.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 5.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 5.5 + 0.5625 Combine like terms: 5.5 + 0.5625 = 6.0625 0.5625 + -1.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -0.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -0.75 = 2.46221445 Simplifying x + -0.75 = 2.46221445 Reorder the terms: -0.75 + x = 2.46221445 Solving -0.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.46221445 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.46221445 + 0.75 x = 2.46221445 + 0.75 Combine like terms: 2.46221445 + 0.75 = 3.21221445 x = 3.21221445 Simplifying x = 3.21221445Subproblem 2
x + -0.75 = -2.46221445 Simplifying x + -0.75 = -2.46221445 Reorder the terms: -0.75 + x = -2.46221445 Solving -0.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.46221445 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.46221445 + 0.75 x = -2.46221445 + 0.75 Combine like terms: -2.46221445 + 0.75 = -1.71221445 x = -1.71221445 Simplifying x = -1.71221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.21221445, -1.71221445}Solution
x = {3.21221445, -1.71221445}
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