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Simplifying 0 = 7 + 37x + -16x2 Solving 0 = 7 + 37x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -37x + 16x2 = 7 + 37x + -16x2 + -7 + -37x + 16x2 Reorder the terms: -7 + -37x + 16x2 = 7 + -7 + 37x + -37x + -16x2 + 16x2 Combine like terms: 7 + -7 = 0 -7 + -37x + 16x2 = 0 + 37x + -37x + -16x2 + 16x2 -7 + -37x + 16x2 = 37x + -37x + -16x2 + 16x2 Combine like terms: 37x + -37x = 0 -7 + -37x + 16x2 = 0 + -16x2 + 16x2 -7 + -37x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -7 + -37x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -2.3125x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -2.3125x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -2.3125x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -2.3125x + x2 = 0 + 0.4375 -2.3125x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -2.3125x + x2 = 0.4375 The x term is -2.3125x. Take half its coefficient (-1.15625). Square it (1.336914063) and add it to both sides. Add '1.336914063' to each side of the equation. -2.3125x + 1.336914063 + x2 = 0.4375 + 1.336914063 Reorder the terms: 1.336914063 + -2.3125x + x2 = 0.4375 + 1.336914063 Combine like terms: 0.4375 + 1.336914063 = 1.774414063 1.336914063 + -2.3125x + x2 = 1.774414063 Factor a perfect square on the left side: (x + -1.15625)(x + -1.15625) = 1.774414063 Calculate the square root of the right side: 1.332071343 Break this problem into two subproblems by setting (x + -1.15625) equal to 1.332071343 and -1.332071343.Subproblem 1
x + -1.15625 = 1.332071343 Simplifying x + -1.15625 = 1.332071343 Reorder the terms: -1.15625 + x = 1.332071343 Solving -1.15625 + x = 1.332071343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + x = 1.332071343 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + x = 1.332071343 + 1.15625 x = 1.332071343 + 1.15625 Combine like terms: 1.332071343 + 1.15625 = 2.488321343 x = 2.488321343 Simplifying x = 2.488321343Subproblem 2
x + -1.15625 = -1.332071343 Simplifying x + -1.15625 = -1.332071343 Reorder the terms: -1.15625 + x = -1.332071343 Solving -1.15625 + x = -1.332071343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + x = -1.332071343 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + x = -1.332071343 + 1.15625 x = -1.332071343 + 1.15625 Combine like terms: -1.332071343 + 1.15625 = -0.175821343 x = -0.175821343 Simplifying x = -0.175821343Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.488321343, -0.175821343}
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