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Simplifying 10 = 7x(x + -18) Reorder the terms: 10 = 7x(-18 + x) 10 = (-18 * 7x + x * 7x) 10 = (-126x + 7x2) Solving 10 = -126x + 7x2 Solving for variable 'x'. Reorder the terms: 10 + 126x + -7x2 = -126x + 126x + 7x2 + -7x2 Combine like terms: -126x + 126x = 0 10 + 126x + -7x2 = 0 + 7x2 + -7x2 10 + 126x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 10 + 126x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.428571429 + -18x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -18x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -18x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -18x + x2 = 0 + 1.428571429 -18x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -18x + x2 = 1.428571429 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 1.428571429 + 81 Reorder the terms: 81 + -18x + x2 = 1.428571429 + 81 Combine like terms: 1.428571429 + 81 = 82.428571429 81 + -18x + x2 = 82.428571429 Factor a perfect square on the left side: (x + -9)(x + -9) = 82.428571429 Calculate the square root of the right side: 9.079018197 Break this problem into two subproblems by setting (x + -9) equal to 9.079018197 and -9.079018197.Subproblem 1
x + -9 = 9.079018197 Simplifying x + -9 = 9.079018197 Reorder the terms: -9 + x = 9.079018197 Solving -9 + x = 9.079018197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.079018197 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.079018197 + 9 x = 9.079018197 + 9 Combine like terms: 9.079018197 + 9 = 18.079018197 x = 18.079018197 Simplifying x = 18.079018197Subproblem 2
x + -9 = -9.079018197 Simplifying x + -9 = -9.079018197 Reorder the terms: -9 + x = -9.079018197 Solving -9 + x = -9.079018197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.079018197 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.079018197 + 9 x = -9.079018197 + 9 Combine like terms: -9.079018197 + 9 = -0.079018197 x = -0.079018197 Simplifying x = -0.079018197Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.079018197, -0.079018197}
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