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Simplifying 45x + 78 = x2 Reorder the terms: 78 + 45x = x2 Solving 78 + 45x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 78 + 45x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -78 + -45x + x2 = 0 Move the constant term to the right: Add '78' to each side of the equation. -78 + -45x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -45x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -45x + x2 = 0 + 78 -45x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -45x + x2 = 78 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = 78 + 506.25 Reorder the terms: 506.25 + -45x + x2 = 78 + 506.25 Combine like terms: 78 + 506.25 = 584.25 506.25 + -45x + x2 = 584.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 584.25 Calculate the square root of the right side: 24.171263931 Break this problem into two subproblems by setting (x + -22.5) equal to 24.171263931 and -24.171263931.Subproblem 1
x + -22.5 = 24.171263931 Simplifying x + -22.5 = 24.171263931 Reorder the terms: -22.5 + x = 24.171263931 Solving -22.5 + x = 24.171263931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 24.171263931 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 24.171263931 + 22.5 x = 24.171263931 + 22.5 Combine like terms: 24.171263931 + 22.5 = 46.671263931 x = 46.671263931 Simplifying x = 46.671263931Subproblem 2
x + -22.5 = -24.171263931 Simplifying x + -22.5 = -24.171263931 Reorder the terms: -22.5 + x = -24.171263931 Solving -22.5 + x = -24.171263931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -24.171263931 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -24.171263931 + 22.5 x = -24.171263931 + 22.5 Combine like terms: -24.171263931 + 22.5 = -1.671263931 x = -1.671263931 Simplifying x = -1.671263931Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.671263931, -1.671263931}
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