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Simplifying 0 = x2(x2 + -19x + -88) Reorder the terms: 0 = x2(-88 + -19x + x2) 0 = (-88 * x2 + -19x * x2 + x2 * x2) 0 = (-88x2 + -19x3 + x4) Solving 0 = -88x2 + -19x3 + x4 Solving for variable 'x'. Remove the zero: 88x2 + 19x3 + -1x4 = -88x2 + -19x3 + x4 + 88x2 + 19x3 + -1x4 Reorder the terms: 88x2 + 19x3 + -1x4 = -88x2 + 88x2 + -19x3 + 19x3 + x4 + -1x4 Combine like terms: -88x2 + 88x2 = 0 88x2 + 19x3 + -1x4 = 0 + -19x3 + 19x3 + x4 + -1x4 88x2 + 19x3 + -1x4 = -19x3 + 19x3 + x4 + -1x4 Combine like terms: -19x3 + 19x3 = 0 88x2 + 19x3 + -1x4 = 0 + x4 + -1x4 88x2 + 19x3 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 88x2 + 19x3 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(88 + 19x + -1x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(88 + 19x + -1x2)' equal to zero and attempt to solve: Simplifying 88 + 19x + -1x2 = 0 Solving 88 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -88 + -19x + x2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + -19x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -19x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -19x + x2 = 0 + 88 -19x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -19x + x2 = 88 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 88 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 88 + 90.25 Combine like terms: 88 + 90.25 = 178.25 90.25 + -19x + x2 = 178.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (x + -9.5) equal to 13.351029923 and -13.351029923.Subproblem 1
x + -9.5 = 13.351029923 Simplifying x + -9.5 = 13.351029923 Reorder the terms: -9.5 + x = 13.351029923 Solving -9.5 + x = 13.351029923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 13.351029923 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 13.351029923 + 9.5 x = 13.351029923 + 9.5 Combine like terms: 13.351029923 + 9.5 = 22.851029923 x = 22.851029923 Simplifying x = 22.851029923Subproblem 2
x + -9.5 = -13.351029923 Simplifying x + -9.5 = -13.351029923 Reorder the terms: -9.5 + x = -13.351029923 Solving -9.5 + x = -13.351029923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -13.351029923 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -13.351029923 + 9.5 x = -13.351029923 + 9.5 Combine like terms: -13.351029923 + 9.5 = -3.851029923 x = -3.851029923 Simplifying x = -3.851029923Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.851029923, -3.851029923}Solution
x = {0, 22.851029923, -3.851029923}
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