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Simplifying x(x + 3) = 143 Reorder the terms: x(3 + x) = 143 (3 * x + x * x) = 143 (3x + x2) = 143 Solving 3x + x2 = 143 Solving for variable 'x'. Reorder the terms: -143 + 3x + x2 = 143 + -143 Combine like terms: 143 + -143 = 0 -143 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '143' to each side of the equation. -143 + 3x + 143 + x2 = 0 + 143 Reorder the terms: -143 + 143 + 3x + x2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + 3x + x2 = 0 + 143 3x + x2 = 0 + 143 Combine like terms: 0 + 143 = 143 3x + x2 = 143 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 = 143 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 143 + 2.25 Combine like terms: 143 + 2.25 = 145.25 2.25 + 3x + x2 = 145.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (x + 1.5) equal to 12.051970793 and -12.051970793.Subproblem 1
x + 1.5 = 12.051970793 Simplifying x + 1.5 = 12.051970793 Reorder the terms: 1.5 + x = 12.051970793 Solving 1.5 + x = 12.051970793 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 = 12.051970793 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.051970793 + -1.5 x = 12.051970793 + -1.5 Combine like terms: 12.051970793 + -1.5 = 10.551970793 x = 10.551970793 Simplifying x = 10.551970793Subproblem 2
x + 1.5 = -12.051970793 Simplifying x + 1.5 = -12.051970793 Reorder the terms: 1.5 + x = -12.051970793 Solving 1.5 + x = -12.051970793 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 = -12.051970793 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.051970793 + -1.5 x = -12.051970793 + -1.5 Combine like terms: -12.051970793 + -1.5 = -13.551970793 x = -13.551970793 Simplifying x = -13.551970793Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.551970793, -13.551970793}
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