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Simplifying 400 = 4x2 + -24x + 32 Reorder the terms: 400 = 32 + -24x + 4x2 Solving 400 = 32 + -24x + 4x2 Solving for variable 'x'. Combine like terms: 400 + -32 = 368 368 + 24x + -4x2 = 32 + -24x + 4x2 + -32 + 24x + -4x2 Reorder the terms: 368 + 24x + -4x2 = 32 + -32 + -24x + 24x + 4x2 + -4x2 Combine like terms: 32 + -32 = 0 368 + 24x + -4x2 = 0 + -24x + 24x + 4x2 + -4x2 368 + 24x + -4x2 = -24x + 24x + 4x2 + -4x2 Combine like terms: -24x + 24x = 0 368 + 24x + -4x2 = 0 + 4x2 + -4x2 368 + 24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 368 + 24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(92 + 6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(92 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 92 + 6x + -1x2 = 0 Solving 92 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -92 + -6x + x2 = 0 Move the constant term to the right: Add '92' to each side of the equation. -92 + -6x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + -6x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + -6x + x2 = 0 + 92 -6x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 -6x + x2 = 92 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 92 + 9 Reorder the terms: 9 + -6x + x2 = 92 + 9 Combine like terms: 92 + 9 = 101 9 + -6x + x2 = 101 Factor a perfect square on the left side: (x + -3)(x + -3) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -3) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -3 = 10.049875621 Simplifying x + -3 = 10.049875621 Reorder the terms: -3 + x = 10.049875621 Solving -3 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 10.049875621 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.049875621 + 3 x = 10.049875621 + 3 Combine like terms: 10.049875621 + 3 = 13.049875621 x = 13.049875621 Simplifying x = 13.049875621Subproblem 2
x + -3 = -10.049875621 Simplifying x + -3 = -10.049875621 Reorder the terms: -3 + x = -10.049875621 Solving -3 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -10.049875621 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.049875621 + 3 x = -10.049875621 + 3 Combine like terms: -10.049875621 + 3 = -7.049875621 x = -7.049875621 Simplifying x = -7.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.049875621, -7.049875621}Solution
x = {13.049875621, -7.049875621}
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