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Simplifying 0 = x2 + 1.5x + -7 Reorder the terms: 0 = -7 + 1.5x + x2 Solving 0 = -7 + 1.5x + x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -1.5x + -1x2 = -7 + 1.5x + x2 + 7 + -1.5x + -1x2 Reorder the terms: 7 + -1.5x + -1x2 = -7 + 7 + 1.5x + -1.5x + x2 + -1x2 Combine like terms: -7 + 7 = 0 7 + -1.5x + -1x2 = 0 + 1.5x + -1.5x + x2 + -1x2 7 + -1.5x + -1x2 = 1.5x + -1.5x + x2 + -1x2 Combine like terms: 1.5x + -1.5x = 0.0 7 + -1.5x + -1x2 = 0.0 + x2 + -1x2 7 + -1.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + -1.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 1.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 1.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 1.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 1.5x + x2 = 0 + 7 1.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 1.5x + x2 = 7 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 7 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 7 + 0.5625 Combine like terms: 7 + 0.5625 = 7.5625 0.5625 + 1.5x + x2 = 7.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (x + 0.75) equal to 2.75 and -2.75.Subproblem 1
x + 0.75 = 2.75 Simplifying x + 0.75 = 2.75 Reorder the terms: 0.75 + x = 2.75 Solving 0.75 + x = 2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.75 + -0.75 x = 2.75 + -0.75 Combine like terms: 2.75 + -0.75 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 0.75 = -2.75 Simplifying x + 0.75 = -2.75 Reorder the terms: 0.75 + x = -2.75 Solving 0.75 + x = -2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.75 + -0.75 x = -2.75 + -0.75 Combine like terms: -2.75 + -0.75 = -3.5 x = -3.5 Simplifying x = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -3.5}
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