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Simplifying -5x2 + -1x + 56 = x + 15 Reorder the terms: 56 + -1x + -5x2 = x + 15 Reorder the terms: 56 + -1x + -5x2 = 15 + x Solving 56 + -1x + -5x2 = 15 + x Solving for variable 'x'. Reorder the terms: 56 + -15 + -1x + -1x + -5x2 = 15 + x + -15 + -1x Combine like terms: 56 + -15 = 41 41 + -1x + -1x + -5x2 = 15 + x + -15 + -1x Combine like terms: -1x + -1x = -2x 41 + -2x + -5x2 = 15 + x + -15 + -1x Reorder the terms: 41 + -2x + -5x2 = 15 + -15 + x + -1x Combine like terms: 15 + -15 = 0 41 + -2x + -5x2 = 0 + x + -1x 41 + -2x + -5x2 = x + -1x Combine like terms: x + -1x = 0 41 + -2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + 0.4x + 8.2 + x2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + 0.4x + x2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + 0.4x + x2 = 0 + 8.2 0.4x + x2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 0.4x + x2 = 8.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 8.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 8.2 + 0.04 Combine like terms: 8.2 + 0.04 = 8.24 0.04 + 0.4x + x2 = 8.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 8.24 Calculate the square root of the right side: 2.870540019 Break this problem into two subproblems by setting (x + 0.2) equal to 2.870540019 and -2.870540019.Subproblem 1
x + 0.2 = 2.870540019 Simplifying x + 0.2 = 2.870540019 Reorder the terms: 0.2 + x = 2.870540019 Solving 0.2 + x = 2.870540019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 2.870540019 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.870540019 + -0.2 x = 2.870540019 + -0.2 Combine like terms: 2.870540019 + -0.2 = 2.670540019 x = 2.670540019 Simplifying x = 2.670540019Subproblem 2
x + 0.2 = -2.870540019 Simplifying x + 0.2 = -2.870540019 Reorder the terms: 0.2 + x = -2.870540019 Solving 0.2 + x = -2.870540019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -2.870540019 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.870540019 + -0.2 x = -2.870540019 + -0.2 Combine like terms: -2.870540019 + -0.2 = -3.070540019 x = -3.070540019 Simplifying x = -3.070540019Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.670540019, -3.070540019}
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