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Simplifying 10x(7 + -1x) = 10(7 + -1x) + x + -63 (7 * 10x + -1x * 10x) = 10(7 + -1x) + x + -63 (70x + -10x2) = 10(7 + -1x) + x + -63 70x + -10x2 = (7 * 10 + -1x * 10) + x + -63 70x + -10x2 = (70 + -10x) + x + -63 Reorder the terms: 70x + -10x2 = 70 + -63 + -10x + x Combine like terms: 70 + -63 = 7 70x + -10x2 = 7 + -10x + x Combine like terms: -10x + x = -9x 70x + -10x2 = 7 + -9x Solving 70x + -10x2 = 7 + -9x Solving for variable 'x'. Reorder the terms: -7 + 70x + 9x + -10x2 = 7 + -9x + -7 + 9x Combine like terms: 70x + 9x = 79x -7 + 79x + -10x2 = 7 + -9x + -7 + 9x Reorder the terms: -7 + 79x + -10x2 = 7 + -7 + -9x + 9x Combine like terms: 7 + -7 = 0 -7 + 79x + -10x2 = 0 + -9x + 9x -7 + 79x + -10x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -7 + 79x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.7 + -7.9x + x2 = 0.0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -7.9x + -0.7 + x2 = 0.0 + -0.7 Reorder the terms: 0.7 + -0.7 + -7.9x + x2 = 0.0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -7.9x + x2 = 0.0 + -0.7 -7.9x + x2 = 0.0 + -0.7 Combine like terms: 0.0 + -0.7 = -0.7 -7.9x + x2 = -0.7 The x term is -7.9x. Take half its coefficient (-3.95). Square it (15.6025) and add it to both sides. Add '15.6025' to each side of the equation. -7.9x + 15.6025 + x2 = -0.7 + 15.6025 Reorder the terms: 15.6025 + -7.9x + x2 = -0.7 + 15.6025 Combine like terms: -0.7 + 15.6025 = 14.9025 15.6025 + -7.9x + x2 = 14.9025 Factor a perfect square on the left side: (x + -3.95)(x + -3.95) = 14.9025 Calculate the square root of the right side: 3.860375629 Break this problem into two subproblems by setting (x + -3.95) equal to 3.860375629 and -3.860375629.Subproblem 1
x + -3.95 = 3.860375629 Simplifying x + -3.95 = 3.860375629 Reorder the terms: -3.95 + x = 3.860375629 Solving -3.95 + x = 3.860375629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.95' to each side of the equation. -3.95 + 3.95 + x = 3.860375629 + 3.95 Combine like terms: -3.95 + 3.95 = 0.00 0.00 + x = 3.860375629 + 3.95 x = 3.860375629 + 3.95 Combine like terms: 3.860375629 + 3.95 = 7.810375629 x = 7.810375629 Simplifying x = 7.810375629Subproblem 2
x + -3.95 = -3.860375629 Simplifying x + -3.95 = -3.860375629 Reorder the terms: -3.95 + x = -3.860375629 Solving -3.95 + x = -3.860375629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.95' to each side of the equation. -3.95 + 3.95 + x = -3.860375629 + 3.95 Combine like terms: -3.95 + 3.95 = 0.00 0.00 + x = -3.860375629 + 3.95 x = -3.860375629 + 3.95 Combine like terms: -3.860375629 + 3.95 = 0.089624371 x = 0.089624371 Simplifying x = 0.089624371Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.810375629, 0.089624371}
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