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Simplifying 2x2 + 7x + -90 = 0 Reorder the terms: -90 + 7x + 2x2 = 0 Solving -90 + 7x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45 + 3.5x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 3.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 3.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 3.5x + x2 = 0 + 45 3.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 3.5x + x2 = 45 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 = 45 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 45 + 3.0625 Combine like terms: 45 + 3.0625 = 48.0625 3.0625 + 3.5x + x2 = 48.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 48.0625 Calculate the square root of the right side: 6.932712312 Break this problem into two subproblems by setting (x + 1.75) equal to 6.932712312 and -6.932712312.Subproblem 1
x + 1.75 = 6.932712312 Simplifying x + 1.75 = 6.932712312 Reorder the terms: 1.75 + x = 6.932712312 Solving 1.75 + x = 6.932712312 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 = 6.932712312 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 6.932712312 + -1.75 x = 6.932712312 + -1.75 Combine like terms: 6.932712312 + -1.75 = 5.182712312 x = 5.182712312 Simplifying x = 5.182712312Subproblem 2
x + 1.75 = -6.932712312 Simplifying x + 1.75 = -6.932712312 Reorder the terms: 1.75 + x = -6.932712312 Solving 1.75 + x = -6.932712312 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 = -6.932712312 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -6.932712312 + -1.75 x = -6.932712312 + -1.75 Combine like terms: -6.932712312 + -1.75 = -8.682712312 x = -8.682712312 Simplifying x = -8.682712312Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.182712312, -8.682712312}
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