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Simplifying 7x(4x + 5) + 2 = 0 Reorder the terms: 7x(5 + 4x) + 2 = 0 (5 * 7x + 4x * 7x) + 2 = 0 (35x + 28x2) + 2 = 0 Reorder the terms: 2 + 35x + 28x2 = 0 Solving 2 + 35x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.07142857143 + 1.25x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + 1.25x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + 1.25x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + 1.25x + x2 = 0 + -0.07142857143 1.25x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 1.25x + x2 = -0.07142857143 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.07142857143 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.07142857143 + 0.390625 Combine like terms: -0.07142857143 + 0.390625 = 0.31919642857 0.390625 + 1.25x + x2 = 0.31919642857 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.31919642857 Calculate the square root of the right side: 0.564974715 Break this problem into two subproblems by setting (x + 0.625) equal to 0.564974715 and -0.564974715.Subproblem 1
x + 0.625 = 0.564974715 Simplifying x + 0.625 = 0.564974715 Reorder the terms: 0.625 + x = 0.564974715 Solving 0.625 + x = 0.564974715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.564974715 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.564974715 + -0.625 x = 0.564974715 + -0.625 Combine like terms: 0.564974715 + -0.625 = -0.060025285 x = -0.060025285 Simplifying x = -0.060025285Subproblem 2
x + 0.625 = -0.564974715 Simplifying x + 0.625 = -0.564974715 Reorder the terms: 0.625 + x = -0.564974715 Solving 0.625 + x = -0.564974715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.564974715 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.564974715 + -0.625 x = -0.564974715 + -0.625 Combine like terms: -0.564974715 + -0.625 = -1.189974715 x = -1.189974715 Simplifying x = -1.189974715Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.060025285, -1.189974715}
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