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Simplifying x2 + -7.2x + -28 = 0 Reorder the terms: -28 + -7.2x + x2 = 0 Solving -28 + -7.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -7.2x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -7.2x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -7.2x + x2 = 0 + 28 -7.2x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -7.2x + x2 = 28 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 28 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 28 + 12.96 Combine like terms: 28 + 12.96 = 40.96 12.96 + -7.2x + x2 = 40.96 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 40.96 Calculate the square root of the right side: 6.4 Break this problem into two subproblems by setting (x + -3.6) equal to 6.4 and -6.4.Subproblem 1
x + -3.6 = 6.4 Simplifying x + -3.6 = 6.4 Reorder the terms: -3.6 + x = 6.4 Solving -3.6 + x = 6.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 6.4 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 6.4 + 3.6 x = 6.4 + 3.6 Combine like terms: 6.4 + 3.6 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -3.6 = -6.4 Simplifying x + -3.6 = -6.4 Reorder the terms: -3.6 + x = -6.4 Solving -3.6 + x = -6.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -6.4 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -6.4 + 3.6 x = -6.4 + 3.6 Combine like terms: -6.4 + 3.6 = -2.8 x = -2.8 Simplifying x = -2.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -2.8}
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