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Simplifying 4x2 + 32x + 15 = 100 Reorder the terms: 15 + 32x + 4x2 = 100 Solving 15 + 32x + 4x2 = 100 Solving for variable 'x'. Reorder the terms: 15 + -100 + 32x + 4x2 = 100 + -100 Combine like terms: 15 + -100 = -85 -85 + 32x + 4x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -85 + 32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -21.25 + 8x + x2 = 0 Move the constant term to the right: Add '21.25' to each side of the equation. -21.25 + 8x + 21.25 + x2 = 0 + 21.25 Reorder the terms: -21.25 + 21.25 + 8x + x2 = 0 + 21.25 Combine like terms: -21.25 + 21.25 = 0.00 0.00 + 8x + x2 = 0 + 21.25 8x + x2 = 0 + 21.25 Combine like terms: 0 + 21.25 = 21.25 8x + x2 = 21.25 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 = 21.25 + 16 Reorder the terms: 16 + 8x + x2 = 21.25 + 16 Combine like terms: 21.25 + 16 = 37.25 16 + 8x + x2 = 37.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 4) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 4 = 6.103277808 Simplifying x + 4 = 6.103277808 Reorder the terms: 4 + x = 6.103277808 Solving 4 + x = 6.103277808 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 = 6.103277808 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.103277808 + -4 x = 6.103277808 + -4 Combine like terms: 6.103277808 + -4 = 2.103277808 x = 2.103277808 Simplifying x = 2.103277808Subproblem 2
x + 4 = -6.103277808 Simplifying x + 4 = -6.103277808 Reorder the terms: 4 + x = -6.103277808 Solving 4 + x = -6.103277808 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 = -6.103277808 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.103277808 + -4 x = -6.103277808 + -4 Combine like terms: -6.103277808 + -4 = -10.103277808 x = -10.103277808 Simplifying x = -10.103277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.103277808, -10.103277808}
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