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Simplifying 8x2 + 10x + -21 = 0 Reorder the terms: -21 + 10x + 8x2 = 0 Solving -21 + 10x + 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 + 1.25x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + 1.25x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + 1.25x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + 1.25x + x2 = 0 + 2.625 1.25x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 1.25x + x2 = 2.625 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 2.625 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 2.625 + 0.390625 Combine like terms: 2.625 + 0.390625 = 3.015625 0.390625 + 1.25x + x2 = 3.015625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + 0.625) equal to 1.736555499 and -1.736555499.Subproblem 1
x + 0.625 = 1.736555499 Simplifying x + 0.625 = 1.736555499 Reorder the terms: 0.625 + x = 1.736555499 Solving 0.625 + x = 1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.736555499 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.736555499 + -0.625 x = 1.736555499 + -0.625 Combine like terms: 1.736555499 + -0.625 = 1.111555499 x = 1.111555499 Simplifying x = 1.111555499Subproblem 2
x + 0.625 = -1.736555499 Simplifying x + 0.625 = -1.736555499 Reorder the terms: 0.625 + x = -1.736555499 Solving 0.625 + x = -1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.736555499 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.736555499 + -0.625 x = -1.736555499 + -0.625 Combine like terms: -1.736555499 + -0.625 = -2.361555499 x = -2.361555499 Simplifying x = -2.361555499Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.111555499, -2.361555499}
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