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Simplifying 8x2 + 11x + -21 = 0 Reorder the terms: -21 + 11x + 8x2 = 0 Solving -21 + 11x + 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'. -2.625 + 1.375x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + 1.375x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + 1.375x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + 1.375x + x2 = 0 + 2.625 1.375x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 1.375x + x2 = 2.625 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 2.625 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 2.625 + 0.47265625 Combine like terms: 2.625 + 0.47265625 = 3.09765625 0.47265625 + 1.375x + x2 = 3.09765625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 3.09765625 Calculate the square root of the right side: 1.76001598 Break this problem into two subproblems by setting (x + 0.6875) equal to 1.76001598 and -1.76001598.Subproblem 1
x + 0.6875 = 1.76001598 Simplifying x + 0.6875 = 1.76001598 Reorder the terms: 0.6875 + x = 1.76001598 Solving 0.6875 + x = 1.76001598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 1.76001598 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 1.76001598 + -0.6875 x = 1.76001598 + -0.6875 Combine like terms: 1.76001598 + -0.6875 = 1.07251598 x = 1.07251598 Simplifying x = 1.07251598Subproblem 2
x + 0.6875 = -1.76001598 Simplifying x + 0.6875 = -1.76001598 Reorder the terms: 0.6875 + x = -1.76001598 Solving 0.6875 + x = -1.76001598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -1.76001598 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -1.76001598 + -0.6875 x = -1.76001598 + -0.6875 Combine like terms: -1.76001598 + -0.6875 = -2.44751598 x = -2.44751598 Simplifying x = -2.44751598Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.07251598, -2.44751598}
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