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Simplifying x2 = 190(0.067 + -1x) x2 = (0.067 * 190 + -1x * 190) x2 = (12.73 + -190x) Solving x2 = 12.73 + -190x Solving for variable 'x'. Reorder the terms: -12.73 + 190x + x2 = 12.73 + -190x + -12.73 + 190x Reorder the terms: -12.73 + 190x + x2 = 12.73 + -12.73 + -190x + 190x Combine like terms: 12.73 + -12.73 = 0.00 -12.73 + 190x + x2 = 0.00 + -190x + 190x -12.73 + 190x + x2 = -190x + 190x Combine like terms: -190x + 190x = 0 -12.73 + 190x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12.73' to each side of the equation. -12.73 + 190x + 12.73 + x2 = 0 + 12.73 Reorder the terms: -12.73 + 12.73 + 190x + x2 = 0 + 12.73 Combine like terms: -12.73 + 12.73 = 0.00 0.00 + 190x + x2 = 0 + 12.73 190x + x2 = 0 + 12.73 Combine like terms: 0 + 12.73 = 12.73 190x + x2 = 12.73 The x term is 190x. Take half its coefficient (95). Square it (9025) and add it to both sides. Add '9025' to each side of the equation. 190x + 9025 + x2 = 12.73 + 9025 Reorder the terms: 9025 + 190x + x2 = 12.73 + 9025 Combine like terms: 12.73 + 9025 = 9037.73 9025 + 190x + x2 = 9037.73 Factor a perfect square on the left side: (x + 95)(x + 95) = 9037.73 Calculate the square root of the right side: 95.06697639 Break this problem into two subproblems by setting (x + 95) equal to 95.06697639 and -95.06697639.Subproblem 1
x + 95 = 95.06697639 Simplifying x + 95 = 95.06697639 Reorder the terms: 95 + x = 95.06697639 Solving 95 + x = 95.06697639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = 95.06697639 + -95 Combine like terms: 95 + -95 = 0 0 + x = 95.06697639 + -95 x = 95.06697639 + -95 Combine like terms: 95.06697639 + -95 = 0.06697639 x = 0.06697639 Simplifying x = 0.06697639Subproblem 2
x + 95 = -95.06697639 Simplifying x + 95 = -95.06697639 Reorder the terms: 95 + x = -95.06697639 Solving 95 + x = -95.06697639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = -95.06697639 + -95 Combine like terms: 95 + -95 = 0 0 + x = -95.06697639 + -95 x = -95.06697639 + -95 Combine like terms: -95.06697639 + -95 = -190.06697639 x = -190.06697639 Simplifying x = -190.06697639Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.06697639, -190.06697639}
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