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Simplifying 5x2 = 34x + -7 Reorder the terms: 5x2 = -7 + 34x Solving 5x2 = -7 + 34x Solving for variable 'x'. Reorder the terms: 7 + -34x + 5x2 = -7 + 34x + 7 + -34x Reorder the terms: 7 + -34x + 5x2 = -7 + 7 + 34x + -34x Combine like terms: -7 + 7 = 0 7 + -34x + 5x2 = 0 + 34x + -34x 7 + -34x + 5x2 = 34x + -34x Combine like terms: 34x + -34x = 0 7 + -34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -6.8x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -6.8x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -6.8x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -6.8x + x2 = 0 + -1.4 -6.8x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -6.8x + x2 = -1.4 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = -1.4 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = -1.4 + 11.56 Combine like terms: -1.4 + 11.56 = 10.16 11.56 + -6.8x + x2 = 10.16 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 10.16 Calculate the square root of the right side: 3.18747549 Break this problem into two subproblems by setting (x + -3.4) equal to 3.18747549 and -3.18747549.Subproblem 1
x + -3.4 = 3.18747549 Simplifying x + -3.4 = 3.18747549 Reorder the terms: -3.4 + x = 3.18747549 Solving -3.4 + x = 3.18747549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 3.18747549 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 3.18747549 + 3.4 x = 3.18747549 + 3.4 Combine like terms: 3.18747549 + 3.4 = 6.58747549 x = 6.58747549 Simplifying x = 6.58747549Subproblem 2
x + -3.4 = -3.18747549 Simplifying x + -3.4 = -3.18747549 Reorder the terms: -3.4 + x = -3.18747549 Solving -3.4 + x = -3.18747549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -3.18747549 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -3.18747549 + 3.4 x = -3.18747549 + 3.4 Combine like terms: -3.18747549 + 3.4 = 0.21252451 x = 0.21252451 Simplifying x = 0.21252451Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.58747549, 0.21252451}
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