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Simplifying 5x2 + 570x + -36 = 0 Reorder the terms: -36 + 570x + 5x2 = 0 Solving -36 + 570x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 114x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 114x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 114x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 114x + x2 = 0 + 7.2 114x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 114x + x2 = 7.2 The x term is 114x. Take half its coefficient (57). Square it (3249) and add it to both sides. Add '3249' to each side of the equation. 114x + 3249 + x2 = 7.2 + 3249 Reorder the terms: 3249 + 114x + x2 = 7.2 + 3249 Combine like terms: 7.2 + 3249 = 3256.2 3249 + 114x + x2 = 3256.2 Factor a perfect square on the left side: (x + 57)(x + 57) = 3256.2 Calculate the square root of the right side: 57.063122943 Break this problem into two subproblems by setting (x + 57) equal to 57.063122943 and -57.063122943.Subproblem 1
x + 57 = 57.063122943 Simplifying x + 57 = 57.063122943 Reorder the terms: 57 + x = 57.063122943 Solving 57 + x = 57.063122943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-57' to each side of the equation. 57 + -57 + x = 57.063122943 + -57 Combine like terms: 57 + -57 = 0 0 + x = 57.063122943 + -57 x = 57.063122943 + -57 Combine like terms: 57.063122943 + -57 = 0.063122943 x = 0.063122943 Simplifying x = 0.063122943Subproblem 2
x + 57 = -57.063122943 Simplifying x + 57 = -57.063122943 Reorder the terms: 57 + x = -57.063122943 Solving 57 + x = -57.063122943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-57' to each side of the equation. 57 + -57 + x = -57.063122943 + -57 Combine like terms: 57 + -57 = 0 0 + x = -57.063122943 + -57 x = -57.063122943 + -57 Combine like terms: -57.063122943 + -57 = -114.063122943 x = -114.063122943 Simplifying x = -114.063122943Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.063122943, -114.063122943}
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