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Simplifying -16x2 + -32x = -380 Reorder the terms: -32x + -16x2 = -380 Solving -32x + -16x2 = -380 Solving for variable 'x'. Reorder the terms: 380 + -32x + -16x2 = -380 + 380 Combine like terms: -380 + 380 = 0 380 + -32x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(95 + -8x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(95 + -8x + -4x2)' equal to zero and attempt to solve: Simplifying 95 + -8x + -4x2 = 0 Solving 95 + -8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -23.75 + 2x + x2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + 2x + 23.75 + x2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + 2x + x2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + 2x + x2 = 0 + 23.75 2x + x2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 2x + x2 = 23.75 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 23.75 + 1 Reorder the terms: 1 + 2x + x2 = 23.75 + 1 Combine like terms: 23.75 + 1 = 24.75 1 + 2x + x2 = 24.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x + 1) equal to 4.974937186 and -4.974937186.Subproblem 1
x + 1 = 4.974937186 Simplifying x + 1 = 4.974937186 Reorder the terms: 1 + x = 4.974937186 Solving 1 + x = 4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.974937186 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.974937186 + -1 x = 4.974937186 + -1 Combine like terms: 4.974937186 + -1 = 3.974937186 x = 3.974937186 Simplifying x = 3.974937186Subproblem 2
x + 1 = -4.974937186 Simplifying x + 1 = -4.974937186 Reorder the terms: 1 + x = -4.974937186 Solving 1 + x = -4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.974937186 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.974937186 + -1 x = -4.974937186 + -1 Combine like terms: -4.974937186 + -1 = -5.974937186 x = -5.974937186 Simplifying x = -5.974937186Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.974937186, -5.974937186}Solution
x = {3.974937186, -5.974937186}
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