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Simplifying 2x2 + 7x + -15 = 10 Reorder the terms: -15 + 7x + 2x2 = 10 Solving -15 + 7x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -15 + -10 + 7x + 2x2 = 10 + -10 Combine like terms: -15 + -10 = -25 -25 + 7x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -25 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 3.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 3.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 3.5x + x2 = 0 + 12.5 3.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 3.5x + x2 = 12.5 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 = 12.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 12.5 + 3.0625 Combine like terms: 12.5 + 3.0625 = 15.5625 3.0625 + 3.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 1.75) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 1.75 = 3.94493346 Simplifying x + 1.75 = 3.94493346 Reorder the terms: 1.75 + x = 3.94493346 Solving 1.75 + x = 3.94493346 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 = 3.94493346 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.94493346 + -1.75 x = 3.94493346 + -1.75 Combine like terms: 3.94493346 + -1.75 = 2.19493346 x = 2.19493346 Simplifying x = 2.19493346Subproblem 2
x + 1.75 = -3.94493346 Simplifying x + 1.75 = -3.94493346 Reorder the terms: 1.75 + x = -3.94493346 Solving 1.75 + x = -3.94493346 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 = -3.94493346 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.94493346 + -1.75 x = -3.94493346 + -1.75 Combine like terms: -3.94493346 + -1.75 = -5.69493346 x = -5.69493346 Simplifying x = -5.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.19493346, -5.69493346}
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