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Simplifying -3x2 + -24x + 17 = -40 Reorder the terms: 17 + -24x + -3x2 = -40 Solving 17 + -24x + -3x2 = -40 Solving for variable 'x'. Reorder the terms: 17 + 40 + -24x + -3x2 = -40 + 40 Combine like terms: 17 + 40 = 57 57 + -24x + -3x2 = -40 + 40 Combine like terms: -40 + 40 = 0 57 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(19 + -8x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(19 + -8x + -1x2)' equal to zero and attempt to solve: Simplifying 19 + -8x + -1x2 = 0 Solving 19 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + 8x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 8x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 8x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 8x + x2 = 0 + 19 8x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 8x + x2 = 19 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 19 + 16 Reorder the terms: 16 + 8x + x2 = 19 + 16 Combine like terms: 19 + 16 = 35 16 + 8x + x2 = 35 Factor a perfect square on the left side: (x + 4)(x + 4) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + 4) equal to 5.916079783 and -5.916079783.Subproblem 1
x + 4 = 5.916079783 Simplifying x + 4 = 5.916079783 Reorder the terms: 4 + x = 5.916079783 Solving 4 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.916079783 + -4 x = 5.916079783 + -4 Combine like terms: 5.916079783 + -4 = 1.916079783 x = 1.916079783 Simplifying x = 1.916079783Subproblem 2
x + 4 = -5.916079783 Simplifying x + 4 = -5.916079783 Reorder the terms: 4 + x = -5.916079783 Solving 4 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.916079783 + -4 x = -5.916079783 + -4 Combine like terms: -5.916079783 + -4 = -9.916079783 x = -9.916079783 Simplifying x = -9.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.916079783, -9.916079783}Solution
x = {1.916079783, -9.916079783}
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