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Simplifying 4x2 + -37x + 36 = 0 Reorder the terms: 36 + -37x + 4x2 = 0 Solving 36 + -37x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + -9.25x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -9.25x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -9.25x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9.25x + x2 = 0 + -9 -9.25x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9.25x + x2 = -9 The x term is -9.25x. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25x + 21.390625 + x2 = -9 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = -9 + 21.390625 Combine like terms: -9 + 21.390625 = 12.390625 21.390625 + -9.25x + x2 = 12.390625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (x + -4.625) equal to 3.52003196 and -3.52003196.Subproblem 1
x + -4.625 = 3.52003196 Simplifying x + -4.625 = 3.52003196 Reorder the terms: -4.625 + x = 3.52003196 Solving -4.625 + x = 3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = 3.52003196 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 3.52003196 + 4.625 x = 3.52003196 + 4.625 Combine like terms: 3.52003196 + 4.625 = 8.14503196 x = 8.14503196 Simplifying x = 8.14503196Subproblem 2
x + -4.625 = -3.52003196 Simplifying x + -4.625 = -3.52003196 Reorder the terms: -4.625 + x = -3.52003196 Solving -4.625 + x = -3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = -3.52003196 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -3.52003196 + 4.625 x = -3.52003196 + 4.625 Combine like terms: -3.52003196 + 4.625 = 1.10496804 x = 1.10496804 Simplifying x = 1.10496804Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.14503196, 1.10496804}
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