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Simplifying 5x2 + -35x = 5x + -8 Reorder the terms: -35x + 5x2 = 5x + -8 Reorder the terms: -35x + 5x2 = -8 + 5x Solving -35x + 5x2 = -8 + 5x Solving for variable 'x'. Reorder the terms: 8 + -35x + -5x + 5x2 = -8 + 5x + 8 + -5x Combine like terms: -35x + -5x = -40x 8 + -40x + 5x2 = -8 + 5x + 8 + -5x Reorder the terms: 8 + -40x + 5x2 = -8 + 8 + 5x + -5x Combine like terms: -8 + 8 = 0 8 + -40x + 5x2 = 0 + 5x + -5x 8 + -40x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 8 + -40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -8x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -8x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -8x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -8x + x2 = 0 + -1.6 -8x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -8x + x2 = -1.6 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 = -1.6 + 16 Reorder the terms: 16 + -8x + x2 = -1.6 + 16 Combine like terms: -1.6 + 16 = 14.4 16 + -8x + x2 = 14.4 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.4 Calculate the square root of the right side: 3.794733192 Break this problem into two subproblems by setting (x + -4) equal to 3.794733192 and -3.794733192.Subproblem 1
x + -4 = 3.794733192 Simplifying x + -4 = 3.794733192 Reorder the terms: -4 + x = 3.794733192 Solving -4 + x = 3.794733192 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 = 3.794733192 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.794733192 + 4 x = 3.794733192 + 4 Combine like terms: 3.794733192 + 4 = 7.794733192 x = 7.794733192 Simplifying x = 7.794733192Subproblem 2
x + -4 = -3.794733192 Simplifying x + -4 = -3.794733192 Reorder the terms: -4 + x = -3.794733192 Solving -4 + x = -3.794733192 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 = -3.794733192 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.794733192 + 4 x = -3.794733192 + 4 Combine like terms: -3.794733192 + 4 = 0.205266808 x = 0.205266808 Simplifying x = 0.205266808Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.794733192, 0.205266808}
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