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Simplifying 0 = -2(8x2 + -15x + -200) Reorder the terms: 0 = -2(-200 + -15x + 8x2) 0 = (-200 * -2 + -15x * -2 + 8x2 * -2) 0 = (400 + 30x + -16x2) Solving 0 = 400 + 30x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -400 = -400 -400 + -30x + 16x2 = 400 + 30x + -16x2 + -400 + -30x + 16x2 Reorder the terms: -400 + -30x + 16x2 = 400 + -400 + 30x + -30x + -16x2 + 16x2 Combine like terms: 400 + -400 = 0 -400 + -30x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -400 + -30x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -400 + -30x + 16x2 = 0 + -16x2 + 16x2 -400 + -30x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -400 + -30x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-200 + -15x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-200 + -15x + 8x2)' equal to zero and attempt to solve: Simplifying -200 + -15x + 8x2 = 0 Solving -200 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -25 + -1.875x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -1.875x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -1.875x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1.875x + x2 = 0 + 25 -1.875x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1.875x + x2 = 25 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 25 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 25 + 0.87890625 Combine like terms: 25 + 0.87890625 = 25.87890625 0.87890625 + -1.875x + x2 = 25.87890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 25.87890625 Calculate the square root of the right side: 5.087131436 Break this problem into two subproblems by setting (x + -0.9375) equal to 5.087131436 and -5.087131436.Subproblem 1
x + -0.9375 = 5.087131436 Simplifying x + -0.9375 = 5.087131436 Reorder the terms: -0.9375 + x = 5.087131436 Solving -0.9375 + x = 5.087131436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 5.087131436 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 5.087131436 + 0.9375 x = 5.087131436 + 0.9375 Combine like terms: 5.087131436 + 0.9375 = 6.024631436 x = 6.024631436 Simplifying x = 6.024631436Subproblem 2
x + -0.9375 = -5.087131436 Simplifying x + -0.9375 = -5.087131436 Reorder the terms: -0.9375 + x = -5.087131436 Solving -0.9375 + x = -5.087131436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -5.087131436 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -5.087131436 + 0.9375 x = -5.087131436 + 0.9375 Combine like terms: -5.087131436 + 0.9375 = -4.149631436 x = -4.149631436 Simplifying x = -4.149631436Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.024631436, -4.149631436}Solution
x = {6.024631436, -4.149631436}
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