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Simplifying 4x2 + -1800 = x + 1800 + 5x Reorder the terms: -1800 + 4x2 = x + 1800 + 5x Reorder the terms: -1800 + 4x2 = 1800 + x + 5x Combine like terms: x + 5x = 6x -1800 + 4x2 = 1800 + 6x Solving -1800 + 4x2 = 1800 + 6x Solving for variable 'x'. Reorder the terms: -1800 + -1800 + -6x + 4x2 = 1800 + 6x + -1800 + -6x Combine like terms: -1800 + -1800 = -3600 -3600 + -6x + 4x2 = 1800 + 6x + -1800 + -6x Reorder the terms: -3600 + -6x + 4x2 = 1800 + -1800 + 6x + -6x Combine like terms: 1800 + -1800 = 0 -3600 + -6x + 4x2 = 0 + 6x + -6x -3600 + -6x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3600 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1800 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1800 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -1800 + -3x + 2x2 = 0 Solving -1800 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -900 + -1.5x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + -1.5x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + -1.5x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + -1.5x + x2 = 0 + 900 -1.5x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 -1.5x + x2 = 900 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 900 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 900 + 0.5625 Combine like terms: 900 + 0.5625 = 900.5625 0.5625 + -1.5x + x2 = 900.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 900.5625 Calculate the square root of the right side: 30.009373536 Break this problem into two subproblems by setting (x + -0.75) equal to 30.009373536 and -30.009373536.Subproblem 1
x + -0.75 = 30.009373536 Simplifying x + -0.75 = 30.009373536 Reorder the terms: -0.75 + x = 30.009373536 Solving -0.75 + x = 30.009373536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 30.009373536 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 30.009373536 + 0.75 x = 30.009373536 + 0.75 Combine like terms: 30.009373536 + 0.75 = 30.759373536 x = 30.759373536 Simplifying x = 30.759373536Subproblem 2
x + -0.75 = -30.009373536 Simplifying x + -0.75 = -30.009373536 Reorder the terms: -0.75 + x = -30.009373536 Solving -0.75 + x = -30.009373536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -30.009373536 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -30.009373536 + 0.75 x = -30.009373536 + 0.75 Combine like terms: -30.009373536 + 0.75 = -29.259373536 x = -29.259373536 Simplifying x = -29.259373536Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.759373536, -29.259373536}Solution
x = {30.759373536, -29.259373536}
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