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Simplifying 5x(5x + 7) = 2x + -3 Reorder the terms: 5x(7 + 5x) = 2x + -3 (7 * 5x + 5x * 5x) = 2x + -3 (35x + 25x2) = 2x + -3 Reorder the terms: 35x + 25x2 = -3 + 2x Solving 35x + 25x2 = -3 + 2x Solving for variable 'x'. Reorder the terms: 3 + 35x + -2x + 25x2 = -3 + 2x + 3 + -2x Combine like terms: 35x + -2x = 33x 3 + 33x + 25x2 = -3 + 2x + 3 + -2x Reorder the terms: 3 + 33x + 25x2 = -3 + 3 + 2x + -2x Combine like terms: -3 + 3 = 0 3 + 33x + 25x2 = 0 + 2x + -2x 3 + 33x + 25x2 = 2x + -2x Combine like terms: 2x + -2x = 0 3 + 33x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.12 + 1.32x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + 1.32x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + 1.32x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + 1.32x + x2 = 0 + -0.12 1.32x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 1.32x + x2 = -0.12 The x term is 1.32x. Take half its coefficient (0.66). Square it (0.4356) and add it to both sides. Add '0.4356' to each side of the equation. 1.32x + 0.4356 + x2 = -0.12 + 0.4356 Reorder the terms: 0.4356 + 1.32x + x2 = -0.12 + 0.4356 Combine like terms: -0.12 + 0.4356 = 0.3156 0.4356 + 1.32x + x2 = 0.3156 Factor a perfect square on the left side: (x + 0.66)(x + 0.66) = 0.3156 Calculate the square root of the right side: 0.561782876 Break this problem into two subproblems by setting (x + 0.66) equal to 0.561782876 and -0.561782876.Subproblem 1
x + 0.66 = 0.561782876 Simplifying x + 0.66 = 0.561782876 Reorder the terms: 0.66 + x = 0.561782876 Solving 0.66 + x = 0.561782876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.66' to each side of the equation. 0.66 + -0.66 + x = 0.561782876 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + x = 0.561782876 + -0.66 x = 0.561782876 + -0.66 Combine like terms: 0.561782876 + -0.66 = -0.098217124 x = -0.098217124 Simplifying x = -0.098217124Subproblem 2
x + 0.66 = -0.561782876 Simplifying x + 0.66 = -0.561782876 Reorder the terms: 0.66 + x = -0.561782876 Solving 0.66 + x = -0.561782876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.66' to each side of the equation. 0.66 + -0.66 + x = -0.561782876 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + x = -0.561782876 + -0.66 x = -0.561782876 + -0.66 Combine like terms: -0.561782876 + -0.66 = -1.221782876 x = -1.221782876 Simplifying x = -1.221782876Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.098217124, -1.221782876}
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