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Simplifying 7x2 = 7 + -4x Solving 7x2 = 7 + -4x Solving for variable 'x'. Reorder the terms: -7 + 4x + 7x2 = 7 + -4x + -7 + 4x Reorder the terms: -7 + 4x + 7x2 = 7 + -7 + -4x + 4x Combine like terms: 7 + -7 = 0 -7 + 4x + 7x2 = 0 + -4x + 4x -7 + 4x + 7x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -7 + 4x + 7x2 = 0 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 = 0.7543014123 x = 0.7543014123 Simplifying x = 0.7543014123Subproblem 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 = -1.3257299837 x = -1.3257299837 Simplifying x = -1.3257299837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7543014123, -1.3257299837}
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