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Simplifying x(x + 2) + -3 = 30 Reorder the terms: x(2 + x) + -3 = 30 (2 * x + x * x) + -3 = 30 (2x + x2) + -3 = 30 Reorder the terms: -3 + 2x + x2 = 30 Solving -3 + 2x + x2 = 30 Solving for variable 'x'. Reorder the terms: -3 + -30 + 2x + x2 = 30 + -30 Combine like terms: -3 + -30 = -33 -33 + 2x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -33 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 2x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 2x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 2x + x2 = 0 + 33 2x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 2x + x2 = 33 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 33 + 1 Reorder the terms: 1 + 2x + x2 = 33 + 1 Combine like terms: 33 + 1 = 34 1 + 2x + x2 = 34 Factor a perfect square on the left side: (x + 1)(x + 1) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 1) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 1 = 5.830951895 Simplifying x + 1 = 5.830951895 Reorder the terms: 1 + x = 5.830951895 Solving 1 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.830951895 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.830951895 + -1 x = 5.830951895 + -1 Combine like terms: 5.830951895 + -1 = 4.830951895 x = 4.830951895 Simplifying x = 4.830951895Subproblem 2
x + 1 = -5.830951895 Simplifying x + 1 = -5.830951895 Reorder the terms: 1 + x = -5.830951895 Solving 1 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.830951895 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.830951895 + -1 x = -5.830951895 + -1 Combine like terms: -5.830951895 + -1 = -6.830951895 x = -6.830951895 Simplifying x = -6.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.830951895, -6.830951895}
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