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Simplifying 210x + 200x2 + -576 = 0 Reorder the terms: -576 + 210x + 200x2 = 0 Solving -576 + 210x + 200x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-288 + 105x + 100x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-288 + 105x + 100x2)' equal to zero and attempt to solve: Simplifying -288 + 105x + 100x2 = 0 Solving -288 + 105x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -2.88 + 1.05x + x2 = 0.00 Move the constant term to the right: Add '2.88' to each side of the equation. -2.88 + 1.05x + 2.88 + x2 = 0.00 + 2.88 Reorder the terms: -2.88 + 2.88 + 1.05x + x2 = 0.00 + 2.88 Combine like terms: -2.88 + 2.88 = 0.00 0.00 + 1.05x + x2 = 0.00 + 2.88 1.05x + x2 = 0.00 + 2.88 Combine like terms: 0.00 + 2.88 = 2.88 1.05x + x2 = 2.88 The x term is 1.05x. Take half its coefficient (0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. 1.05x + 0.275625 + x2 = 2.88 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = 2.88 + 0.275625 Combine like terms: 2.88 + 0.275625 = 3.155625 0.275625 + 1.05x + x2 = 3.155625 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 3.155625 Calculate the square root of the right side: 1.776407892 Break this problem into two subproblems by setting (x + 0.525) equal to 1.776407892 and -1.776407892.Subproblem 1
x + 0.525 = 1.776407892 Simplifying x + 0.525 = 1.776407892 Reorder the terms: 0.525 + x = 1.776407892 Solving 0.525 + x = 1.776407892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 1.776407892 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 1.776407892 + -0.525 x = 1.776407892 + -0.525 Combine like terms: 1.776407892 + -0.525 = 1.251407892 x = 1.251407892 Simplifying x = 1.251407892Subproblem 2
x + 0.525 = -1.776407892 Simplifying x + 0.525 = -1.776407892 Reorder the terms: 0.525 + x = -1.776407892 Solving 0.525 + x = -1.776407892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -1.776407892 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -1.776407892 + -0.525 x = -1.776407892 + -0.525 Combine like terms: -1.776407892 + -0.525 = -2.301407892 x = -2.301407892 Simplifying x = -2.301407892Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.251407892, -2.301407892}Solution
x = {1.251407892, -2.301407892}
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