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Simplifying 8x2 + -28x + -24 = 0 Reorder the terms: -24 + -28x + 8x2 = 0 Solving -24 + -28x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -7x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + -7x + 2x2 = 0 Solving -6 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -3.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -3.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.5x + x2 = 0 + 3 -3.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.5x + x2 = 3 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 3 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 3 + 3.0625 Combine like terms: 3 + 3.0625 = 6.0625 3.0625 + -3.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -1.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -1.75 = 2.46221445 Simplifying x + -1.75 = 2.46221445 Reorder the terms: -1.75 + x = 2.46221445 Solving -1.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.46221445 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.46221445 + 1.75 x = 2.46221445 + 1.75 Combine like terms: 2.46221445 + 1.75 = 4.21221445 x = 4.21221445 Simplifying x = 4.21221445Subproblem 2
x + -1.75 = -2.46221445 Simplifying x + -1.75 = -2.46221445 Reorder the terms: -1.75 + x = -2.46221445 Solving -1.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.46221445 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.46221445 + 1.75 x = -2.46221445 + 1.75 Combine like terms: -2.46221445 + 1.75 = -0.71221445 x = -0.71221445 Simplifying x = -0.71221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.21221445, -0.71221445}Solution
x = {4.21221445, -0.71221445}
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