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Simplifying 7x2 + 10x = 39 Reorder the terms: 10x + 7x2 = 39 Solving 10x + 7x2 = 39 Solving for variable 'x'. Reorder the terms: -39 + 10x + 7x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + 10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.571428571 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '5.571428571' to each side of the equation. -5.571428571 + 1.428571429x + 5.571428571 + x2 = 0 + 5.571428571 Reorder the terms: -5.571428571 + 5.571428571 + 1.428571429x + x2 = 0 + 5.571428571 Combine like terms: -5.571428571 + 5.571428571 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + 5.571428571 1.428571429x + x2 = 0 + 5.571428571 Combine like terms: 0 + 5.571428571 = 5.571428571 1.428571429x + x2 = 5.571428571 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 5.571428571 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 5.571428571 + 0.5102040819 Combine like terms: 5.571428571 + 0.5102040819 = 6.0816326529 0.5102040819 + 1.428571429x + x2 = 6.0816326529 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 6.0816326529 Calculate the square root of the right side: 2.466096643 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 2.466096643 and -2.466096643.Subproblem 1
x + 0.7142857145 = 2.466096643 Simplifying x + 0.7142857145 = 2.466096643 Reorder the terms: 0.7142857145 + x = 2.466096643 Solving 0.7142857145 + x = 2.466096643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 2.466096643 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 2.466096643 + -0.7142857145 x = 2.466096643 + -0.7142857145 Combine like terms: 2.466096643 + -0.7142857145 = 1.7518109285 x = 1.7518109285 Simplifying x = 1.7518109285Subproblem 2
x + 0.7142857145 = -2.466096643 Simplifying x + 0.7142857145 = -2.466096643 Reorder the terms: 0.7142857145 + x = -2.466096643 Solving 0.7142857145 + x = -2.466096643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -2.466096643 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -2.466096643 + -0.7142857145 x = -2.466096643 + -0.7142857145 Combine like terms: -2.466096643 + -0.7142857145 = -3.1803823575 x = -3.1803823575 Simplifying x = -3.1803823575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7518109285, -3.1803823575}
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