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Simplifying -5x2 + 56 = x + 15 Reorder the terms: 56 + -5x2 = x + 15 Reorder the terms: 56 + -5x2 = 15 + x Solving 56 + -5x2 = 15 + x Solving for variable 'x'. Reorder the terms: 56 + -15 + -1x + -5x2 = 15 + x + -15 + -1x Combine like terms: 56 + -15 = 41 41 + -1x + -5x2 = 15 + x + -15 + -1x Reorder the terms: 41 + -1x + -5x2 = 15 + -15 + x + -1x Combine like terms: 15 + -15 = 0 41 + -1x + -5x2 = 0 + x + -1x 41 + -1x + -5x2 = x + -1x Combine like terms: x + -1x = 0 41 + -1x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.2 + 0.2x + x2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + 0.2x + 8.2 + x2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + 0.2x + x2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + 0.2x + x2 = 0 + 8.2 0.2x + x2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 0.2x + x2 = 8.2 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 8.2 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 8.2 + 0.01 Combine like terms: 8.2 + 0.01 = 8.21 0.01 + 0.2x + x2 = 8.21 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 8.21 Calculate the square root of the right side: 2.865309756 Break this problem into two subproblems by setting (x + 0.1) equal to 2.865309756 and -2.865309756.Subproblem 1
x + 0.1 = 2.865309756 Simplifying x + 0.1 = 2.865309756 Reorder the terms: 0.1 + x = 2.865309756 Solving 0.1 + x = 2.865309756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.865309756 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.865309756 + -0.1 x = 2.865309756 + -0.1 Combine like terms: 2.865309756 + -0.1 = 2.765309756 x = 2.765309756 Simplifying x = 2.765309756Subproblem 2
x + 0.1 = -2.865309756 Simplifying x + 0.1 = -2.865309756 Reorder the terms: 0.1 + x = -2.865309756 Solving 0.1 + x = -2.865309756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.865309756 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.865309756 + -0.1 x = -2.865309756 + -0.1 Combine like terms: -2.865309756 + -0.1 = -2.965309756 x = -2.965309756 Simplifying x = -2.965309756Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.765309756, -2.965309756}
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