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Simplifying 5x2 + -3 + 4x + -12x2 + 20 + -7x = 0 Reorder the terms: -3 + 20 + 4x + -7x + 5x2 + -12x2 = 0 Combine like terms: -3 + 20 = 17 17 + 4x + -7x + 5x2 + -12x2 = 0 Combine like terms: 4x + -7x = -3x 17 + -3x + 5x2 + -12x2 = 0 Combine like terms: 5x2 + -12x2 = -7x2 17 + -3x + -7x2 = 0 Solving 17 + -3x + -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'. -2.428571429 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '2.428571429' to each side of the equation. -2.428571429 + 0.4285714286x + 2.428571429 + x2 = 0 + 2.428571429 Reorder the terms: -2.428571429 + 2.428571429 + 0.4285714286x + x2 = 0 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 2.428571429 0.4285714286x + x2 = 0 + 2.428571429 Combine like terms: 0 + 2.428571429 = 2.428571429 0.4285714286x + x2 = 2.428571429 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 2.428571429 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 2.428571429 + 0.04591836735 Combine like terms: 2.428571429 + 0.04591836735 = 2.47448979635 0.04591836735 + 0.4285714286x + x2 = 2.47448979635 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 2.47448979635 Calculate the square root of the right side: 1.573051111 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.573051111 and -1.573051111.Subproblem 1
x + 0.2142857143 = 1.573051111 Simplifying x + 0.2142857143 = 1.573051111 Reorder the terms: 0.2142857143 + x = 1.573051111 Solving 0.2142857143 + x = 1.573051111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 1.573051111 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.573051111 + -0.2142857143 x = 1.573051111 + -0.2142857143 Combine like terms: 1.573051111 + -0.2142857143 = 1.3587653967 x = 1.3587653967 Simplifying x = 1.3587653967Subproblem 2
x + 0.2142857143 = -1.573051111 Simplifying x + 0.2142857143 = -1.573051111 Reorder the terms: 0.2142857143 + x = -1.573051111 Solving 0.2142857143 + x = -1.573051111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -1.573051111 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.573051111 + -0.2142857143 x = -1.573051111 + -0.2142857143 Combine like terms: -1.573051111 + -0.2142857143 = -1.7873368253 x = -1.7873368253 Simplifying x = -1.7873368253Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3587653967, -1.7873368253}
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