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Simplifying 16x2 + 40x + -1.5 = 0 Reorder the terms: -1.5 + 40x + 16x2 = 0 Solving -1.5 + 40x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.09375 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + 2.5x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + 2.5x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + 2.5x + x2 = 0 + 0.09375 2.5x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 2.5x + x2 = 0.09375 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.09375 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.09375 + 1.5625 Combine like terms: 0.09375 + 1.5625 = 1.65625 1.5625 + 2.5x + x2 = 1.65625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.65625 Calculate the square root of the right side: 1.286953768 Break this problem into two subproblems by setting (x + 1.25) equal to 1.286953768 and -1.286953768.Subproblem 1
x + 1.25 = 1.286953768 Simplifying x + 1.25 = 1.286953768 Reorder the terms: 1.25 + x = 1.286953768 Solving 1.25 + x = 1.286953768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.286953768 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.286953768 + -1.25 x = 1.286953768 + -1.25 Combine like terms: 1.286953768 + -1.25 = 0.036953768 x = 0.036953768 Simplifying x = 0.036953768Subproblem 2
x + 1.25 = -1.286953768 Simplifying x + 1.25 = -1.286953768 Reorder the terms: 1.25 + x = -1.286953768 Solving 1.25 + x = -1.286953768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.286953768 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.286953768 + -1.25 x = -1.286953768 + -1.25 Combine like terms: -1.286953768 + -1.25 = -2.536953768 x = -2.536953768 Simplifying x = -2.536953768Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.036953768, -2.536953768}
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