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Simplifying 8x2 + -16x + -15 = 0 Reorder the terms: -15 + -16x + 8x2 = 0 Solving -15 + -16x + 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'. -1.875 + -2x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -2x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -2x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -2x + x2 = 0 + 1.875 -2x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -2x + x2 = 1.875 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.875 + 1 Reorder the terms: 1 + -2x + x2 = 1.875 + 1 Combine like terms: 1.875 + 1 = 2.875 1 + -2x + x2 = 2.875 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + -1) equal to 1.695582496 and -1.695582496.Subproblem 1
x + -1 = 1.695582496 Simplifying x + -1 = 1.695582496 Reorder the terms: -1 + x = 1.695582496 Solving -1 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.695582496 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.695582496 + 1 x = 1.695582496 + 1 Combine like terms: 1.695582496 + 1 = 2.695582496 x = 2.695582496 Simplifying x = 2.695582496Subproblem 2
x + -1 = -1.695582496 Simplifying x + -1 = -1.695582496 Reorder the terms: -1 + x = -1.695582496 Solving -1 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.695582496 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.695582496 + 1 x = -1.695582496 + 1 Combine like terms: -1.695582496 + 1 = -0.695582496 x = -0.695582496 Simplifying x = -0.695582496Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.695582496, -0.695582496}
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