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Simplifying x2 + 75x + -84 = 0 Reorder the terms: -84 + 75x + x2 = 0 Solving -84 + 75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 75x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 75x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 75x + x2 = 0 + 84 75x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 75x + x2 = 84 The x term is 75x. Take half its coefficient (37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. 75x + 1406.25 + x2 = 84 + 1406.25 Reorder the terms: 1406.25 + 75x + x2 = 84 + 1406.25 Combine like terms: 84 + 1406.25 = 1490.25 1406.25 + 75x + x2 = 1490.25 Factor a perfect square on the left side: (x + 37.5)(x + 37.5) = 1490.25 Calculate the square root of the right side: 38.603756294 Break this problem into two subproblems by setting (x + 37.5) equal to 38.603756294 and -38.603756294.Subproblem 1
x + 37.5 = 38.603756294 Simplifying x + 37.5 = 38.603756294 Reorder the terms: 37.5 + x = 38.603756294 Solving 37.5 + x = 38.603756294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = 38.603756294 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = 38.603756294 + -37.5 x = 38.603756294 + -37.5 Combine like terms: 38.603756294 + -37.5 = 1.103756294 x = 1.103756294 Simplifying x = 1.103756294Subproblem 2
x + 37.5 = -38.603756294 Simplifying x + 37.5 = -38.603756294 Reorder the terms: 37.5 + x = -38.603756294 Solving 37.5 + x = -38.603756294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = -38.603756294 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = -38.603756294 + -37.5 x = -38.603756294 + -37.5 Combine like terms: -38.603756294 + -37.5 = -76.103756294 x = -76.103756294 Simplifying x = -76.103756294Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.103756294, -76.103756294}
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