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Simplifying 8x2 + 15x + -5 = 0 Reorder the terms: -5 + 15x + 8x2 = 0 Solving -5 + 15x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 1.875x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.875x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.875x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.875x + x2 = 0 + 0.625 1.875x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.875x + x2 = 0.625 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = 0.625 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = 0.625 + 0.87890625 Combine like terms: 0.625 + 0.87890625 = 1.50390625 0.87890625 + 1.875x + x2 = 1.50390625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 1.50390625 Calculate the square root of the right side: 1.226338554 Break this problem into two subproblems by setting (x + 0.9375) equal to 1.226338554 and -1.226338554.Subproblem 1
x + 0.9375 = 1.226338554 Simplifying x + 0.9375 = 1.226338554 Reorder the terms: 0.9375 + x = 1.226338554 Solving 0.9375 + x = 1.226338554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 1.226338554 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 1.226338554 + -0.9375 x = 1.226338554 + -0.9375 Combine like terms: 1.226338554 + -0.9375 = 0.288838554 x = 0.288838554 Simplifying x = 0.288838554Subproblem 2
x + 0.9375 = -1.226338554 Simplifying x + 0.9375 = -1.226338554 Reorder the terms: 0.9375 + x = -1.226338554 Solving 0.9375 + x = -1.226338554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -1.226338554 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -1.226338554 + -0.9375 x = -1.226338554 + -0.9375 Combine like terms: -1.226338554 + -0.9375 = -2.163838554 x = -2.163838554 Simplifying x = -2.163838554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288838554, -2.163838554}
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