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Simplifying 7x2 + -4x + -400 = 0 Reorder the terms: -400 + -4x + 7x2 = 0 Solving -400 + -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'. -57.14285714 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '57.14285714' to each side of the equation. -57.14285714 + -0.5714285714x + 57.14285714 + x2 = 0 + 57.14285714 Reorder the terms: -57.14285714 + 57.14285714 + -0.5714285714x + x2 = 0 + 57.14285714 Combine like terms: -57.14285714 + 57.14285714 = 0.00000000 0.00000000 + -0.5714285714x + x2 = 0 + 57.14285714 -0.5714285714x + x2 = 0 + 57.14285714 Combine like terms: 0 + 57.14285714 = 57.14285714 -0.5714285714x + x2 = 57.14285714 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 = 57.14285714 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 57.14285714 + 0.08163265305 Combine like terms: 57.14285714 + 0.08163265305 = 57.22448979305 0.08163265305 + -0.5714285714x + x2 = 57.22448979305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 57.22448979305 Calculate the square root of the right side: 7.564687025 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 7.564687025 and -7.564687025.Subproblem 1
x + -0.2857142857 = 7.564687025 Simplifying x + -0.2857142857 = 7.564687025 Reorder the terms: -0.2857142857 + x = 7.564687025 Solving -0.2857142857 + x = 7.564687025 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 = 7.564687025 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 7.564687025 + 0.2857142857 x = 7.564687025 + 0.2857142857 Combine like terms: 7.564687025 + 0.2857142857 = 7.8504013107 x = 7.8504013107 Simplifying x = 7.8504013107Subproblem 2
x + -0.2857142857 = -7.564687025 Simplifying x + -0.2857142857 = -7.564687025 Reorder the terms: -0.2857142857 + x = -7.564687025 Solving -0.2857142857 + x = -7.564687025 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 = -7.564687025 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -7.564687025 + 0.2857142857 x = -7.564687025 + 0.2857142857 Combine like terms: -7.564687025 + 0.2857142857 = -7.2789727393 x = -7.2789727393 Simplifying x = -7.2789727393Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.8504013107, -7.2789727393}
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