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Simplifying 13x + -10x * 10x = 0.4 Reorder the terms for easier multiplication: 13x + -10 * 10x * x = 0.4 Multiply -10 * 10 13x + -100x * x = 0.4 Multiply x * x 13x + -100x2 = 0.4 Solving 13x + -100x2 = 0.4 Solving for variable 'x'. Reorder the terms: -0.4 + 13x + -100x2 = 0.4 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 -0.4 + 13x + -100x2 = 0.0 Begin completing the square. Divide all terms by -100 the coefficient of the squared term: Divide each side by '-100'. 0.004 + -0.13x + x2 = 0.000 Move the constant term to the right: Add '-0.004' to each side of the equation. 0.004 + -0.13x + -0.004 + x2 = 0.000 + -0.004 Reorder the terms: 0.004 + -0.004 + -0.13x + x2 = 0.000 + -0.004 Combine like terms: 0.004 + -0.004 = 0.000 0.000 + -0.13x + x2 = 0.000 + -0.004 -0.13x + x2 = 0.000 + -0.004 Combine like terms: 0.000 + -0.004 = -0.004 -0.13x + x2 = -0.004 The x term is -0.13x. Take half its coefficient (-0.065). Square it (0.004225) and add it to both sides. Add '0.004225' to each side of the equation. -0.13x + 0.004225 + x2 = -0.004 + 0.004225 Reorder the terms: 0.004225 + -0.13x + x2 = -0.004 + 0.004225 Combine like terms: -0.004 + 0.004225 = 0.000225 0.004225 + -0.13x + x2 = 0.000225 Factor a perfect square on the left side: (x + -0.065)(x + -0.065) = 0.000225 Calculate the square root of the right side: 0.015 Break this problem into two subproblems by setting (x + -0.065) equal to 0.015 and -0.015.Subproblem 1
x + -0.065 = 0.015 Simplifying x + -0.065 = 0.015 Reorder the terms: -0.065 + x = 0.015 Solving -0.065 + x = 0.015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.065' to each side of the equation. -0.065 + 0.065 + x = 0.015 + 0.065 Combine like terms: -0.065 + 0.065 = 0.000 0.000 + x = 0.015 + 0.065 x = 0.015 + 0.065 Combine like terms: 0.015 + 0.065 = 0.08 x = 0.08 Simplifying x = 0.08Subproblem 2
x + -0.065 = -0.015 Simplifying x + -0.065 = -0.015 Reorder the terms: -0.065 + x = -0.015 Solving -0.065 + x = -0.015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.065' to each side of the equation. -0.065 + 0.065 + x = -0.015 + 0.065 Combine like terms: -0.065 + 0.065 = 0.000 0.000 + x = -0.015 + 0.065 x = -0.015 + 0.065 Combine like terms: -0.015 + 0.065 = 0.05 x = 0.05 Simplifying x = 0.05Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08, 0.05}
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