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Simplifying 7x2 + -5x + -84 = 0 Reorder the terms: -84 + -5x + 7x2 = 0 Solving -84 + -5x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.7142857143x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.7142857143x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.7142857143x + x2 = 0 + 12 -0.7142857143x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.7142857143x + x2 = 12 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 = 12 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 12 + 0.1275510204 Combine like terms: 12 + 0.1275510204 = 12.1275510204 0.1275510204 + -0.7142857143x + x2 = 12.1275510204 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 12.1275510204 Calculate the square root of the right side: 3.482463355 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 3.482463355 and -3.482463355.Subproblem 1
x + -0.3571428572 = 3.482463355 Simplifying x + -0.3571428572 = 3.482463355 Reorder the terms: -0.3571428572 + x = 3.482463355 Solving -0.3571428572 + x = 3.482463355 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 = 3.482463355 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 3.482463355 + 0.3571428572 x = 3.482463355 + 0.3571428572 Combine like terms: 3.482463355 + 0.3571428572 = 3.8396062122 x = 3.8396062122 Simplifying x = 3.8396062122Subproblem 2
x + -0.3571428572 = -3.482463355 Simplifying x + -0.3571428572 = -3.482463355 Reorder the terms: -0.3571428572 + x = -3.482463355 Solving -0.3571428572 + x = -3.482463355 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 = -3.482463355 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -3.482463355 + 0.3571428572 x = -3.482463355 + 0.3571428572 Combine like terms: -3.482463355 + 0.3571428572 = -3.1253204978 x = -3.1253204978 Simplifying x = -3.1253204978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8396062122, -3.1253204978}
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