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Simplifying 14x2 + 12x = 87 Reorder the terms: 12x + 14x2 = 87 Solving 12x + 14x2 = 87 Solving for variable 'x'. Reorder the terms: -87 + 12x + 14x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + 12x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -6.214285714 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '6.214285714' to each side of the equation. -6.214285714 + 0.8571428571x + 6.214285714 + x2 = 0 + 6.214285714 Reorder the terms: -6.214285714 + 6.214285714 + 0.8571428571x + x2 = 0 + 6.214285714 Combine like terms: -6.214285714 + 6.214285714 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + 6.214285714 0.8571428571x + x2 = 0 + 6.214285714 Combine like terms: 0 + 6.214285714 = 6.214285714 0.8571428571x + x2 = 6.214285714 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = 6.214285714 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 6.214285714 + 0.1836734694 Combine like terms: 6.214285714 + 0.1836734694 = 6.3979591834 0.1836734694 + 0.8571428571x + x2 = 6.3979591834 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 6.3979591834 Calculate the square root of the right side: 2.529418744 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 2.529418744 and -2.529418744.Subproblem 1
x + 0.4285714286 = 2.529418744 Simplifying x + 0.4285714286 = 2.529418744 Reorder the terms: 0.4285714286 + x = 2.529418744 Solving 0.4285714286 + x = 2.529418744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 2.529418744 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 2.529418744 + -0.4285714286 x = 2.529418744 + -0.4285714286 Combine like terms: 2.529418744 + -0.4285714286 = 2.1008473154 x = 2.1008473154 Simplifying x = 2.1008473154Subproblem 2
x + 0.4285714286 = -2.529418744 Simplifying x + 0.4285714286 = -2.529418744 Reorder the terms: 0.4285714286 + x = -2.529418744 Solving 0.4285714286 + x = -2.529418744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -2.529418744 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -2.529418744 + -0.4285714286 x = -2.529418744 + -0.4285714286 Combine like terms: -2.529418744 + -0.4285714286 = -2.9579901726 x = -2.9579901726 Simplifying x = -2.9579901726Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1008473154, -2.9579901726}
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