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Simplifying -10x2 + 2.5x + 5 = -1 Reorder the terms: 5 + 2.5x + -10x2 = -1 Solving 5 + 2.5x + -10x2 = -1 Solving for variable 'x'. Reorder the terms: 5 + 1 + 2.5x + -10x2 = -1 + 1 Combine like terms: 5 + 1 = 6 6 + 2.5x + -10x2 = -1 + 1 Combine like terms: -1 + 1 = 0 6 + 2.5x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.6 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.25x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.25x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.25x + x2 = 0 + 0.6 -0.25x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.25x + x2 = 0.6 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.6 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.6 + 0.015625 Combine like terms: 0.6 + 0.015625 = 0.615625 0.015625 + -0.25x + x2 = 0.615625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.615625 Calculate the square root of the right side: 0.784617741 Break this problem into two subproblems by setting (x + -0.125) equal to 0.784617741 and -0.784617741.Subproblem 1
x + -0.125 = 0.784617741 Simplifying x + -0.125 = 0.784617741 Reorder the terms: -0.125 + x = 0.784617741 Solving -0.125 + x = 0.784617741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.784617741 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.784617741 + 0.125 x = 0.784617741 + 0.125 Combine like terms: 0.784617741 + 0.125 = 0.909617741 x = 0.909617741 Simplifying x = 0.909617741Subproblem 2
x + -0.125 = -0.784617741 Simplifying x + -0.125 = -0.784617741 Reorder the terms: -0.125 + x = -0.784617741 Solving -0.125 + x = -0.784617741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.784617741 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.784617741 + 0.125 x = -0.784617741 + 0.125 Combine like terms: -0.784617741 + 0.125 = -0.659617741 x = -0.659617741 Simplifying x = -0.659617741Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.909617741, -0.659617741}
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