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Simplifying 45x2 + 86x + 36 = -4x + 2x Reorder the terms: 36 + 86x + 45x2 = -4x + 2x Combine like terms: -4x + 2x = -2x 36 + 86x + 45x2 = -2x Solving 36 + 86x + 45x2 = -2x Solving for variable 'x'. Reorder the terms: 36 + 86x + 2x + 45x2 = -2x + 2x Combine like terms: 86x + 2x = 88x 36 + 88x + 45x2 = -2x + 2x Combine like terms: -2x + 2x = 0 36 + 88x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 0.8 + 1.955555556x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 1.955555556x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 1.955555556x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 1.955555556x + x2 = 0 + -0.8 1.955555556x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 1.955555556x + x2 = -0.8 The x term is 1.955555556x. Take half its coefficient (0.977777778). Square it (0.9560493832) and add it to both sides. Add '0.9560493832' to each side of the equation. 1.955555556x + 0.9560493832 + x2 = -0.8 + 0.9560493832 Reorder the terms: 0.9560493832 + 1.955555556x + x2 = -0.8 + 0.9560493832 Combine like terms: -0.8 + 0.9560493832 = 0.1560493832 0.9560493832 + 1.955555556x + x2 = 0.1560493832 Factor a perfect square on the left side: (x + 0.977777778)(x + 0.977777778) = 0.1560493832 Calculate the square root of the right side: 0.395030864 Break this problem into two subproblems by setting (x + 0.977777778) equal to 0.395030864 and -0.395030864.Subproblem 1
x + 0.977777778 = 0.395030864 Simplifying x + 0.977777778 = 0.395030864 Reorder the terms: 0.977777778 + x = 0.395030864 Solving 0.977777778 + x = 0.395030864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.977777778' to each side of the equation. 0.977777778 + -0.977777778 + x = 0.395030864 + -0.977777778 Combine like terms: 0.977777778 + -0.977777778 = 0.000000000 0.000000000 + x = 0.395030864 + -0.977777778 x = 0.395030864 + -0.977777778 Combine like terms: 0.395030864 + -0.977777778 = -0.582746914 x = -0.582746914 Simplifying x = -0.582746914Subproblem 2
x + 0.977777778 = -0.395030864 Simplifying x + 0.977777778 = -0.395030864 Reorder the terms: 0.977777778 + x = -0.395030864 Solving 0.977777778 + x = -0.395030864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.977777778' to each side of the equation. 0.977777778 + -0.977777778 + x = -0.395030864 + -0.977777778 Combine like terms: 0.977777778 + -0.977777778 = 0.000000000 0.000000000 + x = -0.395030864 + -0.977777778 x = -0.395030864 + -0.977777778 Combine like terms: -0.395030864 + -0.977777778 = -1.372808642 x = -1.372808642 Simplifying x = -1.372808642Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.582746914, -1.372808642}
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