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Simplifying (2x)(2x) + -5x = 3000 Remove parenthesis around (2x) 2x(2x) + -5x = 3000 Remove parenthesis around (2x) 2x * 2x + -5x = 3000 Reorder the terms for easier multiplication: 2 * 2x * x + -5x = 3000 Multiply 2 * 2 4x * x + -5x = 3000 Multiply x * x 4x2 + -5x = 3000 Reorder the terms: -5x + 4x2 = 3000 Solving -5x + 4x2 = 3000 Solving for variable 'x'. Reorder the terms: -3000 + -5x + 4x2 = 3000 + -3000 Combine like terms: 3000 + -3000 = 0 -3000 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -750 + -1.25x + x2 = 0 Move the constant term to the right: Add '750' to each side of the equation. -750 + -1.25x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + -1.25x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -1.25x + x2 = 0 + 750 -1.25x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 -1.25x + x2 = 750 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 750 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 750 + 0.390625 Combine like terms: 750 + 0.390625 = 750.390625 0.390625 + -1.25x + x2 = 750.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 750.390625 Calculate the square root of the right side: 27.393258751 Break this problem into two subproblems by setting (x + -0.625) equal to 27.393258751 and -27.393258751.Subproblem 1
x + -0.625 = 27.393258751 Simplifying x + -0.625 = 27.393258751 Reorder the terms: -0.625 + x = 27.393258751 Solving -0.625 + x = 27.393258751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 27.393258751 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 27.393258751 + 0.625 x = 27.393258751 + 0.625 Combine like terms: 27.393258751 + 0.625 = 28.018258751 x = 28.018258751 Simplifying x = 28.018258751Subproblem 2
x + -0.625 = -27.393258751 Simplifying x + -0.625 = -27.393258751 Reorder the terms: -0.625 + x = -27.393258751 Solving -0.625 + x = -27.393258751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -27.393258751 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -27.393258751 + 0.625 x = -27.393258751 + 0.625 Combine like terms: -27.393258751 + 0.625 = -26.768258751 x = -26.768258751 Simplifying x = -26.768258751Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.018258751, -26.768258751}
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