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Simplifying 4x2 + -45x + 112 = 0 Reorder the terms: 112 + -45x + 4x2 = 0 Solving 112 + -45x + 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'. 28 + -11.25x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -11.25x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -11.25x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -11.25x + x2 = 0 + -28 -11.25x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -11.25x + x2 = -28 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = -28 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = -28 + 31.640625 Combine like terms: -28 + 31.640625 = 3.640625 31.640625 + -11.25x + x2 = 3.640625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + -5.625) equal to 1.90804219 and -1.90804219.Subproblem 1
x + -5.625 = 1.90804219 Simplifying x + -5.625 = 1.90804219 Reorder the terms: -5.625 + x = 1.90804219 Solving -5.625 + x = 1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 1.90804219 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 1.90804219 + 5.625 x = 1.90804219 + 5.625 Combine like terms: 1.90804219 + 5.625 = 7.53304219 x = 7.53304219 Simplifying x = 7.53304219Subproblem 2
x + -5.625 = -1.90804219 Simplifying x + -5.625 = -1.90804219 Reorder the terms: -5.625 + x = -1.90804219 Solving -5.625 + x = -1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -1.90804219 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -1.90804219 + 5.625 x = -1.90804219 + 5.625 Combine like terms: -1.90804219 + 5.625 = 3.71695781 x = 3.71695781 Simplifying x = 3.71695781Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.53304219, 3.71695781}
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