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Simplifying 3.66(0.12 + -0.70x + x2) = x (0.12 * 3.66 + -0.70x * 3.66 + x2 * 3.66) = x (0.4392 + -2.562x + 3.66x2) = x Solving 0.4392 + -2.562x + 3.66x2 = x Solving for variable 'x'. Reorder the terms: 0.4392 + -2.562x + -1x + 3.66x2 = x + -1x Combine like terms: -2.562x + -1x = -3.562x 0.4392 + -3.562x + 3.66x2 = x + -1x Combine like terms: x + -1x = 0 0.4392 + -3.562x + 3.66x2 = 0 Begin completing the square. Divide all terms by 3.66 the coefficient of the squared term: Divide each side by '3.66'. 0.12 + -0.9732240437x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.9732240437x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.9732240437x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.9732240437x + x2 = 0 + -0.12 -0.9732240437x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.9732240437x + x2 = -0.12 The x term is -0.9732240437x. Take half its coefficient (-0.4866120219). Square it (0.2367912599) and add it to both sides. Add '0.2367912599' to each side of the equation. -0.9732240437x + 0.2367912599 + x2 = -0.12 + 0.2367912599 Reorder the terms: 0.2367912599 + -0.9732240437x + x2 = -0.12 + 0.2367912599 Combine like terms: -0.12 + 0.2367912599 = 0.1167912599 0.2367912599 + -0.9732240437x + x2 = 0.1167912599 Factor a perfect square on the left side: (x + -0.4866120219)(x + -0.4866120219) = 0.1167912599 Calculate the square root of the right side: 0.341747363 Break this problem into two subproblems by setting (x + -0.4866120219) equal to 0.341747363 and -0.341747363.Subproblem 1
x + -0.4866120219 = 0.341747363 Simplifying x + -0.4866120219 = 0.341747363 Reorder the terms: -0.4866120219 + x = 0.341747363 Solving -0.4866120219 + x = 0.341747363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4866120219' to each side of the equation. -0.4866120219 + 0.4866120219 + x = 0.341747363 + 0.4866120219 Combine like terms: -0.4866120219 + 0.4866120219 = 0.0000000000 0.0000000000 + x = 0.341747363 + 0.4866120219 x = 0.341747363 + 0.4866120219 Combine like terms: 0.341747363 + 0.4866120219 = 0.8283593849 x = 0.8283593849 Simplifying x = 0.8283593849Subproblem 2
x + -0.4866120219 = -0.341747363 Simplifying x + -0.4866120219 = -0.341747363 Reorder the terms: -0.4866120219 + x = -0.341747363 Solving -0.4866120219 + x = -0.341747363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4866120219' to each side of the equation. -0.4866120219 + 0.4866120219 + x = -0.341747363 + 0.4866120219 Combine like terms: -0.4866120219 + 0.4866120219 = 0.0000000000 0.0000000000 + x = -0.341747363 + 0.4866120219 x = -0.341747363 + 0.4866120219 Combine like terms: -0.341747363 + 0.4866120219 = 0.1448646589 x = 0.1448646589 Simplifying x = 0.1448646589Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8283593849, 0.1448646589}
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