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Simplifying 7x2 + 3 = 7 + -40x Reorder the terms: 3 + 7x2 = 7 + -40x Solving 3 + 7x2 = 7 + -40x Solving for variable 'x'. Reorder the terms: 3 + -7 + 40x + 7x2 = 7 + -40x + -7 + 40x Combine like terms: 3 + -7 = -4 -4 + 40x + 7x2 = 7 + -40x + -7 + 40x Reorder the terms: -4 + 40x + 7x2 = 7 + -7 + -40x + 40x Combine like terms: 7 + -7 = 0 -4 + 40x + 7x2 = 0 + -40x + 40x -4 + 40x + 7x2 = -40x + 40x Combine like terms: -40x + 40x = 0 -4 + 40x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 5.714285714x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 5.714285714x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 5.714285714x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 5.714285714x + x2 = 0 + 0.5714285714 5.714285714x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 5.714285714x + x2 = 0.5714285714 The x term is 5.714285714x. Take half its coefficient (2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. 5.714285714x + 8.163265305 + x2 = 0.5714285714 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714x + x2 = 0.5714285714 + 8.163265305 Combine like terms: 0.5714285714 + 8.163265305 = 8.7346938764 8.163265305 + 5.714285714x + x2 = 8.7346938764 Factor a perfect square on the left side: (x + 2.857142857)(x + 2.857142857) = 8.7346938764 Calculate the square root of the right side: 2.955451552 Break this problem into two subproblems by setting (x + 2.857142857) equal to 2.955451552 and -2.955451552.Subproblem 1
x + 2.857142857 = 2.955451552 Simplifying x + 2.857142857 = 2.955451552 Reorder the terms: 2.857142857 + x = 2.955451552 Solving 2.857142857 + x = 2.955451552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = 2.955451552 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = 2.955451552 + -2.857142857 x = 2.955451552 + -2.857142857 Combine like terms: 2.955451552 + -2.857142857 = 0.098308695 x = 0.098308695 Simplifying x = 0.098308695Subproblem 2
x + 2.857142857 = -2.955451552 Simplifying x + 2.857142857 = -2.955451552 Reorder the terms: 2.857142857 + x = -2.955451552 Solving 2.857142857 + x = -2.955451552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = -2.955451552 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = -2.955451552 + -2.857142857 x = -2.955451552 + -2.857142857 Combine like terms: -2.955451552 + -2.857142857 = -5.812594409 x = -5.812594409 Simplifying x = -5.812594409Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.098308695, -5.812594409}
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