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Simplifying 10x + x2 = 56.25 Solving 10x + x2 = 56.25 Solving for variable 'x'. Reorder the terms: -56.25 + 10x + x2 = 56.25 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 -56.25 + 10x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + 10x + 56.25 + x2 = 0.00 + 56.25 Reorder the terms: -56.25 + 56.25 + 10x + x2 = 0.00 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + 10x + x2 = 0.00 + 56.25 10x + x2 = 0.00 + 56.25 Combine like terms: 0.00 + 56.25 = 56.25 10x + x2 = 56.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 56.25 + 25 Reorder the terms: 25 + 10x + x2 = 56.25 + 25 Combine like terms: 56.25 + 25 = 81.25 25 + 10x + x2 = 81.25 Factor a perfect square on the left side: (x + 5)(x + 5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 5 = 9.013878189 Simplifying x + 5 = 9.013878189 Reorder the terms: 5 + x = 9.013878189 Solving 5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.013878189 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.013878189 + -5 x = 9.013878189 + -5 Combine like terms: 9.013878189 + -5 = 4.013878189 x = 4.013878189 Simplifying x = 4.013878189Subproblem 2
x + 5 = -9.013878189 Simplifying x + 5 = -9.013878189 Reorder the terms: 5 + x = -9.013878189 Solving 5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.013878189 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.013878189 + -5 x = -9.013878189 + -5 Combine like terms: -9.013878189 + -5 = -14.013878189 x = -14.013878189 Simplifying x = -14.013878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.013878189, -14.013878189}
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