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Simplifying 1.5 = (-0.0001x2 + 0.0542x + 1.1784) Reorder the terms: 1.5 = (1.1784 + 0.0542x + -0.0001x2) Remove parenthesis around (1.1784 + 0.0542x + -0.0001x2) 1.5 = 1.1784 + 0.0542x + -0.0001x2 Solving 1.5 = 1.1784 + 0.0542x + -0.0001x2 Solving for variable 'x'. Combine like terms: 1.5 + -1.1784 = 0.3216 0.3216 + -0.0542x + 0.0001x2 = 1.1784 + 0.0542x + -0.0001x2 + -1.1784 + -0.0542x + 0.0001x2 Reorder the terms: 0.3216 + -0.0542x + 0.0001x2 = 1.1784 + -1.1784 + 0.0542x + -0.0542x + -0.0001x2 + 0.0001x2 Combine like terms: 1.1784 + -1.1784 = 0.0000 0.3216 + -0.0542x + 0.0001x2 = 0.0000 + 0.0542x + -0.0542x + -0.0001x2 + 0.0001x2 0.3216 + -0.0542x + 0.0001x2 = 0.0542x + -0.0542x + -0.0001x2 + 0.0001x2 Combine like terms: 0.0542x + -0.0542x = 0.0000 0.3216 + -0.0542x + 0.0001x2 = 0.0000 + -0.0001x2 + 0.0001x2 0.3216 + -0.0542x + 0.0001x2 = -0.0001x2 + 0.0001x2 Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000 0.3216 + -0.0542x + 0.0001x2 = 0.0000 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. 3216 + -542x + x2 = 0 Move the constant term to the right: Add '-3216' to each side of the equation. 3216 + -542x + -3216 + x2 = 0 + -3216 Reorder the terms: 3216 + -3216 + -542x + x2 = 0 + -3216 Combine like terms: 3216 + -3216 = 0 0 + -542x + x2 = 0 + -3216 -542x + x2 = 0 + -3216 Combine like terms: 0 + -3216 = -3216 -542x + x2 = -3216 The x term is -542x. Take half its coefficient (-271). Square it (73441) and add it to both sides. Add '73441' to each side of the equation. -542x + 73441 + x2 = -3216 + 73441 Reorder the terms: 73441 + -542x + x2 = -3216 + 73441 Combine like terms: -3216 + 73441 = 70225 73441 + -542x + x2 = 70225 Factor a perfect square on the left side: (x + -271)(x + -271) = 70225 Calculate the square root of the right side: 265 Break this problem into two subproblems by setting (x + -271) equal to 265 and -265.Subproblem 1
x + -271 = 265 Simplifying x + -271 = 265 Reorder the terms: -271 + x = 265 Solving -271 + x = 265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '271' to each side of the equation. -271 + 271 + x = 265 + 271 Combine like terms: -271 + 271 = 0 0 + x = 265 + 271 x = 265 + 271 Combine like terms: 265 + 271 = 536 x = 536 Simplifying x = 536Subproblem 2
x + -271 = -265 Simplifying x + -271 = -265 Reorder the terms: -271 + x = -265 Solving -271 + x = -265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '271' to each side of the equation. -271 + 271 + x = -265 + 271 Combine like terms: -271 + 271 = 0 0 + x = -265 + 271 x = -265 + 271 Combine like terms: -265 + 271 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {536, 6}
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