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Simplifying 0 = -7x2 + 5x + 8 Reorder the terms: 0 = 8 + 5x + -7x2 Solving 0 = 8 + 5x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -5x + 7x2 = 8 + 5x + -7x2 + -8 + -5x + 7x2 Reorder the terms: -8 + -5x + 7x2 = 8 + -8 + 5x + -5x + -7x2 + 7x2 Combine like terms: 8 + -8 = 0 -8 + -5x + 7x2 = 0 + 5x + -5x + -7x2 + 7x2 -8 + -5x + 7x2 = 5x + -5x + -7x2 + 7x2 Combine like terms: 5x + -5x = 0 -8 + -5x + 7x2 = 0 + -7x2 + 7x2 -8 + -5x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -8 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.7142857143x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.7142857143x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 1.142857143 -0.7142857143x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.7142857143x + x2 = 1.142857143 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 1.142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 1.142857143 + 0.1275510204 Combine like terms: 1.142857143 + 0.1275510204 = 1.2704081634 0.1275510204 + -0.7142857143x + x2 = 1.2704081634 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.2704081634 Calculate the square root of the right side: 1.127123846 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.127123846 and -1.127123846.Subproblem 1
x + -0.3571428572 = 1.127123846 Simplifying x + -0.3571428572 = 1.127123846 Reorder the terms: -0.3571428572 + x = 1.127123846 Solving -0.3571428572 + x = 1.127123846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.127123846 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.127123846 + 0.3571428572 x = 1.127123846 + 0.3571428572 Combine like terms: 1.127123846 + 0.3571428572 = 1.4842667032 x = 1.4842667032 Simplifying x = 1.4842667032Subproblem 2
x + -0.3571428572 = -1.127123846 Simplifying x + -0.3571428572 = -1.127123846 Reorder the terms: -0.3571428572 + x = -1.127123846 Solving -0.3571428572 + x = -1.127123846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.127123846 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.127123846 + 0.3571428572 x = -1.127123846 + 0.3571428572 Combine like terms: -1.127123846 + 0.3571428572 = -0.7699809888 x = -0.7699809888 Simplifying x = -0.7699809888Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4842667032, -0.7699809888}
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