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Simplifying 2x2 + 7x = 420 Reorder the terms: 7x + 2x2 = 420 Solving 7x + 2x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 7x + 2x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -210 + 3.5x + x2 = 0 Move the constant term to the right: Add '210' to each side of the equation. -210 + 3.5x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + 3.5x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 3.5x + x2 = 0 + 210 3.5x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 3.5x + x2 = 210 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 210 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 210 + 3.0625 Combine like terms: 210 + 3.0625 = 213.0625 3.0625 + 3.5x + x2 = 213.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 213.0625 Calculate the square root of the right side: 14.596660577 Break this problem into two subproblems by setting (x + 1.75) equal to 14.596660577 and -14.596660577.Subproblem 1
x + 1.75 = 14.596660577 Simplifying x + 1.75 = 14.596660577 Reorder the terms: 1.75 + x = 14.596660577 Solving 1.75 + x = 14.596660577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 14.596660577 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 14.596660577 + -1.75 x = 14.596660577 + -1.75 Combine like terms: 14.596660577 + -1.75 = 12.846660577 x = 12.846660577 Simplifying x = 12.846660577Subproblem 2
x + 1.75 = -14.596660577 Simplifying x + 1.75 = -14.596660577 Reorder the terms: 1.75 + x = -14.596660577 Solving 1.75 + x = -14.596660577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -14.596660577 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -14.596660577 + -1.75 x = -14.596660577 + -1.75 Combine like terms: -14.596660577 + -1.75 = -16.346660577 x = -16.346660577 Simplifying x = -16.346660577Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.846660577, -16.346660577}
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