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Simplifying (x + -7.5)(x + 4.3) = 0 Reorder the terms: (-7.5 + x)(x + 4.3) = 0 Reorder the terms: (-7.5 + x)(4.3 + x) = 0 Multiply (-7.5 + x) * (4.3 + x) (-7.5(4.3 + x) + x(4.3 + x)) = 0 ((4.3 * -7.5 + x * -7.5) + x(4.3 + x)) = 0 ((-32.25 + -7.5x) + x(4.3 + x)) = 0 (-32.25 + -7.5x + (4.3 * x + x * x)) = 0 (-32.25 + -7.5x + (4.3x + x2)) = 0 Combine like terms: -7.5x + 4.3x = -3.2x (-32.25 + -3.2x + x2) = 0 Solving -32.25 + -3.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32.25' to each side of the equation. -32.25 + -3.2x + 32.25 + x2 = 0 + 32.25 Reorder the terms: -32.25 + 32.25 + -3.2x + x2 = 0 + 32.25 Combine like terms: -32.25 + 32.25 = 0.00 0.00 + -3.2x + x2 = 0 + 32.25 -3.2x + x2 = 0 + 32.25 Combine like terms: 0 + 32.25 = 32.25 -3.2x + x2 = 32.25 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 32.25 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 32.25 + 2.56 Combine like terms: 32.25 + 2.56 = 34.81 2.56 + -3.2x + x2 = 34.81 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 34.81 Calculate the square root of the right side: 5.9 Break this problem into two subproblems by setting (x + -1.6) equal to 5.9 and -5.9.Subproblem 1
x + -1.6 = 5.9 Simplifying x + -1.6 = 5.9 Reorder the terms: -1.6 + x = 5.9 Solving -1.6 + x = 5.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 5.9 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 5.9 + 1.6 x = 5.9 + 1.6 Combine like terms: 5.9 + 1.6 = 7.5 x = 7.5 Simplifying x = 7.5Subproblem 2
x + -1.6 = -5.9 Simplifying x + -1.6 = -5.9 Reorder the terms: -1.6 + x = -5.9 Solving -1.6 + x = -5.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -5.9 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -5.9 + 1.6 x = -5.9 + 1.6 Combine like terms: -5.9 + 1.6 = -4.3 x = -4.3 Simplifying x = -4.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.5, -4.3}
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