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Simplifying x(x + 3) = 57 Reorder the terms: x(3 + x) = 57 (3 * x + x * x) = 57 (3x + x2) = 57 Solving 3x + x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + 3x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + 3x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + 3x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 3x + x2 = 0 + 57 3x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 3x + x2 = 57 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 57 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 57 + 2.25 Combine like terms: 57 + 2.25 = 59.25 2.25 + 3x + x2 = 59.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + 1.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + 1.5 = 7.697402159 Simplifying x + 1.5 = 7.697402159 Reorder the terms: 1.5 + x = 7.697402159 Solving 1.5 + x = 7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.697402159 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.697402159 + -1.5 x = 7.697402159 + -1.5 Combine like terms: 7.697402159 + -1.5 = 6.197402159 x = 6.197402159 Simplifying x = 6.197402159Subproblem 2
x + 1.5 = -7.697402159 Simplifying x + 1.5 = -7.697402159 Reorder the terms: 1.5 + x = -7.697402159 Solving 1.5 + x = -7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.697402159 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.697402159 + -1.5 x = -7.697402159 + -1.5 Combine like terms: -7.697402159 + -1.5 = -9.197402159 x = -9.197402159 Simplifying x = -9.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.197402159, -9.197402159}
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