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Simplifying 2x2 + 14x + -15 = 0 Reorder the terms: -15 + 14x + 2x2 = 0 Solving -15 + 14x + 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'. -7.5 + 7x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 7x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 7x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 7x + x2 = 0 + 7.5 7x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 7x + x2 = 7.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 7.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 7.5 + 12.25 Combine like terms: 7.5 + 12.25 = 19.75 12.25 + 7x + x2 = 19.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + 3.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + 3.5 = 4.444097209 Simplifying x + 3.5 = 4.444097209 Reorder the terms: 3.5 + x = 4.444097209 Solving 3.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.444097209 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.444097209 + -3.5 x = 4.444097209 + -3.5 Combine like terms: 4.444097209 + -3.5 = 0.944097209 x = 0.944097209 Simplifying x = 0.944097209Subproblem 2
x + 3.5 = -4.444097209 Simplifying x + 3.5 = -4.444097209 Reorder the terms: 3.5 + x = -4.444097209 Solving 3.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.444097209 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.444097209 + -3.5 x = -4.444097209 + -3.5 Combine like terms: -4.444097209 + -3.5 = -7.944097209 x = -7.944097209 Simplifying x = -7.944097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.944097209, -7.944097209}
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