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Simplifying (5x + -3)(5x + -3) = 31 Reorder the terms: (-3 + 5x)(5x + -3) = 31 Reorder the terms: (-3 + 5x)(-3 + 5x) = 31 Multiply (-3 + 5x) * (-3 + 5x) (-3(-3 + 5x) + 5x * (-3 + 5x)) = 31 ((-3 * -3 + 5x * -3) + 5x * (-3 + 5x)) = 31 ((9 + -15x) + 5x * (-3 + 5x)) = 31 (9 + -15x + (-3 * 5x + 5x * 5x)) = 31 (9 + -15x + (-15x + 25x2)) = 31 Combine like terms: -15x + -15x = -30x (9 + -30x + 25x2) = 31 Solving 9 + -30x + 25x2 = 31 Solving for variable 'x'. Reorder the terms: 9 + -31 + -30x + 25x2 = 31 + -31 Combine like terms: 9 + -31 = -22 -22 + -30x + 25x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -22 + -30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.88 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.88' to each side of the equation. -0.88 + -1.2x + 0.88 + x2 = 0 + 0.88 Reorder the terms: -0.88 + 0.88 + -1.2x + x2 = 0 + 0.88 Combine like terms: -0.88 + 0.88 = 0.00 0.00 + -1.2x + x2 = 0 + 0.88 -1.2x + x2 = 0 + 0.88 Combine like terms: 0 + 0.88 = 0.88 -1.2x + x2 = 0.88 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.88 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.88 + 0.36 Combine like terms: 0.88 + 0.36 = 1.24 0.36 + -1.2x + x2 = 1.24 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + -0.6) equal to 1.113552873 and -1.113552873.Subproblem 1
x + -0.6 = 1.113552873 Simplifying x + -0.6 = 1.113552873 Reorder the terms: -0.6 + x = 1.113552873 Solving -0.6 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.113552873 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.113552873 + 0.6 x = 1.113552873 + 0.6 Combine like terms: 1.113552873 + 0.6 = 1.713552873 x = 1.713552873 Simplifying x = 1.713552873Subproblem 2
x + -0.6 = -1.113552873 Simplifying x + -0.6 = -1.113552873 Reorder the terms: -0.6 + x = -1.113552873 Solving -0.6 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.113552873 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.113552873 + 0.6 x = -1.113552873 + 0.6 Combine like terms: -1.113552873 + 0.6 = -0.513552873 x = -0.513552873 Simplifying x = -0.513552873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.713552873, -0.513552873}
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