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Simplifying 8x = 5x2 + -15 Reorder the terms: 8x = -15 + 5x2 Solving 8x = -15 + 5x2 Solving for variable 'x'. Reorder the terms: 15 + 8x + -5x2 = -15 + 5x2 + 15 + -5x2 Reorder the terms: 15 + 8x + -5x2 = -15 + 15 + 5x2 + -5x2 Combine like terms: -15 + 15 = 0 15 + 8x + -5x2 = 0 + 5x2 + -5x2 15 + 8x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 15 + 8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3 + -1.6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.6x + x2 = 0 + 3 -1.6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.6x + x2 = 3 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 3 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 3 + 0.64 Combine like terms: 3 + 0.64 = 3.64 0.64 + -1.6x + x2 = 3.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 3.64 Calculate the square root of the right side: 1.907878403 Break this problem into two subproblems by setting (x + -0.8) equal to 1.907878403 and -1.907878403.Subproblem 1
x + -0.8 = 1.907878403 Simplifying x + -0.8 = 1.907878403 Reorder the terms: -0.8 + x = 1.907878403 Solving -0.8 + x = 1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.907878403 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.907878403 + 0.8 x = 1.907878403 + 0.8 Combine like terms: 1.907878403 + 0.8 = 2.707878403 x = 2.707878403 Simplifying x = 2.707878403Subproblem 2
x + -0.8 = -1.907878403 Simplifying x + -0.8 = -1.907878403 Reorder the terms: -0.8 + x = -1.907878403 Solving -0.8 + x = -1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.907878403 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.907878403 + 0.8 x = -1.907878403 + 0.8 Combine like terms: -1.907878403 + 0.8 = -1.107878403 x = -1.107878403 Simplifying x = -1.107878403Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.707878403, -1.107878403}
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