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Simplifying -7x2 + 4x + 7 = 0 Reorder the terms: 7 + 4x + -7x2 = 0 Solving 7 + 4x + -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'. -1 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5714285714x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5714285714x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5714285714x + x2 = 0 + 1 -0.5714285714x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5714285714x + x2 = 1 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 1 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 1 + 0.08163265305 Combine like terms: 1 + 0.08163265305 = 1.08163265305 0.08163265305 + -0.5714285714x + x2 = 1.08163265305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 1.08163265305 Calculate the square root of the right side: 1.040015698 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.040015698 and -1.040015698.Subproblem 1
x + -0.2857142857 = 1.040015698 Simplifying x + -0.2857142857 = 1.040015698 Reorder the terms: -0.2857142857 + x = 1.040015698 Solving -0.2857142857 + x = 1.040015698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.040015698 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.040015698 + 0.2857142857 x = 1.040015698 + 0.2857142857 Combine like terms: 1.040015698 + 0.2857142857 = 1.3257299837 x = 1.3257299837 Simplifying x = 1.3257299837Subproblem 2
x + -0.2857142857 = -1.040015698 Simplifying x + -0.2857142857 = -1.040015698 Reorder the terms: -0.2857142857 + x = -1.040015698 Solving -0.2857142857 + x = -1.040015698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.040015698 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.040015698 + 0.2857142857 x = -1.040015698 + 0.2857142857 Combine like terms: -1.040015698 + 0.2857142857 = -0.7543014123 x = -0.7543014123 Simplifying x = -0.7543014123Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3257299837, -0.7543014123}
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