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Simplifying 2x2 + 7x = 120 Reorder the terms: 7x + 2x2 = 120 Solving 7x + 2x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 7x + 2x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60 + 3.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 3.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 3.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 3.5x + x2 = 0 + 60 3.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 3.5x + x2 = 60 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 = 60 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 60 + 3.0625 Combine like terms: 60 + 3.0625 = 63.0625 3.0625 + 3.5x + x2 = 63.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (x + 1.75) equal to 7.941190087 and -7.941190087.Subproblem 1
x + 1.75 = 7.941190087 Simplifying x + 1.75 = 7.941190087 Reorder the terms: 1.75 + x = 7.941190087 Solving 1.75 + x = 7.941190087 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 = 7.941190087 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 7.941190087 + -1.75 x = 7.941190087 + -1.75 Combine like terms: 7.941190087 + -1.75 = 6.191190087 x = 6.191190087 Simplifying x = 6.191190087Subproblem 2
x + 1.75 = -7.941190087 Simplifying x + 1.75 = -7.941190087 Reorder the terms: 1.75 + x = -7.941190087 Solving 1.75 + x = -7.941190087 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 = -7.941190087 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -7.941190087 + -1.75 x = -7.941190087 + -1.75 Combine like terms: -7.941190087 + -1.75 = -9.691190087 x = -9.691190087 Simplifying x = -9.691190087Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.191190087, -9.691190087}
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