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Simplifying 8x2 = 15 + -4x Solving 8x2 = 15 + -4x Solving for variable 'x'. Reorder the terms: -15 + 4x + 8x2 = 15 + -4x + -15 + 4x Reorder the terms: -15 + 4x + 8x2 = 15 + -15 + -4x + 4x Combine like terms: 15 + -15 = 0 -15 + 4x + 8x2 = 0 + -4x + 4x -15 + 4x + 8x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -15 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.5x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.5x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.5x + x2 = 0 + 1.875 0.5x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.5x + x2 = 1.875 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.875 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.875 + 0.0625 Combine like terms: 1.875 + 0.0625 = 1.9375 0.0625 + 0.5x + x2 = 1.9375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.9375 Calculate the square root of the right side: 1.391941091 Break this problem into two subproblems by setting (x + 0.25) equal to 1.391941091 and -1.391941091.Subproblem 1
x + 0.25 = 1.391941091 Simplifying x + 0.25 = 1.391941091 Reorder the terms: 0.25 + x = 1.391941091 Solving 0.25 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.391941091 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.391941091 + -0.25 x = 1.391941091 + -0.25 Combine like terms: 1.391941091 + -0.25 = 1.141941091 x = 1.141941091 Simplifying x = 1.141941091Subproblem 2
x + 0.25 = -1.391941091 Simplifying x + 0.25 = -1.391941091 Reorder the terms: 0.25 + x = -1.391941091 Solving 0.25 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.391941091 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.391941091 + -0.25 x = -1.391941091 + -0.25 Combine like terms: -1.391941091 + -0.25 = -1.641941091 x = -1.641941091 Simplifying x = -1.641941091Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.141941091, -1.641941091}
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