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Simplifying 7 = 43x + 2x2 Solving 7 = 43x + 2x2 Solving for variable 'x'. Reorder the terms: 7 + -43x + -2x2 = 43x + -43x + 2x2 + -2x2 Combine like terms: 43x + -43x = 0 7 + -43x + -2x2 = 0 + 2x2 + -2x2 7 + -43x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + -43x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + 21.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 21.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 21.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 21.5x + x2 = 0 + 3.5 21.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 21.5x + x2 = 3.5 The x term is 21.5x. Take half its coefficient (10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. 21.5x + 115.5625 + x2 = 3.5 + 115.5625 Reorder the terms: 115.5625 + 21.5x + x2 = 3.5 + 115.5625 Combine like terms: 3.5 + 115.5625 = 119.0625 115.5625 + 21.5x + x2 = 119.0625 Factor a perfect square on the left side: (x + 10.75)(x + 10.75) = 119.0625 Calculate the square root of the right side: 10.911576421 Break this problem into two subproblems by setting (x + 10.75) equal to 10.911576421 and -10.911576421.Subproblem 1
x + 10.75 = 10.911576421 Simplifying x + 10.75 = 10.911576421 Reorder the terms: 10.75 + x = 10.911576421 Solving 10.75 + x = 10.911576421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = 10.911576421 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = 10.911576421 + -10.75 x = 10.911576421 + -10.75 Combine like terms: 10.911576421 + -10.75 = 0.161576421 x = 0.161576421 Simplifying x = 0.161576421Subproblem 2
x + 10.75 = -10.911576421 Simplifying x + 10.75 = -10.911576421 Reorder the terms: 10.75 + x = -10.911576421 Solving 10.75 + x = -10.911576421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = -10.911576421 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = -10.911576421 + -10.75 x = -10.911576421 + -10.75 Combine like terms: -10.911576421 + -10.75 = -21.661576421 x = -21.661576421 Simplifying x = -21.661576421Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.161576421, -21.661576421}
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