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Simplifying 1764 = 2x2 + 5x Reorder the terms: 1764 = 5x + 2x2 Solving 1764 = 5x + 2x2 Solving for variable 'x'. Reorder the terms: 1764 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 1764 + -5x + -2x2 = 0 + 2x2 + -2x2 1764 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1764 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -882 + 2.5x + x2 = 0 Move the constant term to the right: Add '882' to each side of the equation. -882 + 2.5x + 882 + x2 = 0 + 882 Reorder the terms: -882 + 882 + 2.5x + x2 = 0 + 882 Combine like terms: -882 + 882 = 0 0 + 2.5x + x2 = 0 + 882 2.5x + x2 = 0 + 882 Combine like terms: 0 + 882 = 882 2.5x + x2 = 882 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 882 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 882 + 1.5625 Combine like terms: 882 + 1.5625 = 883.5625 1.5625 + 2.5x + x2 = 883.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 883.5625 Calculate the square root of the right side: 29.724779225 Break this problem into two subproblems by setting (x + 1.25) equal to 29.724779225 and -29.724779225.Subproblem 1
x + 1.25 = 29.724779225 Simplifying x + 1.25 = 29.724779225 Reorder the terms: 1.25 + x = 29.724779225 Solving 1.25 + x = 29.724779225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 29.724779225 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 29.724779225 + -1.25 x = 29.724779225 + -1.25 Combine like terms: 29.724779225 + -1.25 = 28.474779225 x = 28.474779225 Simplifying x = 28.474779225Subproblem 2
x + 1.25 = -29.724779225 Simplifying x + 1.25 = -29.724779225 Reorder the terms: 1.25 + x = -29.724779225 Solving 1.25 + x = -29.724779225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -29.724779225 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -29.724779225 + -1.25 x = -29.724779225 + -1.25 Combine like terms: -29.724779225 + -1.25 = -30.974779225 x = -30.974779225 Simplifying x = -30.974779225Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.474779225, -30.974779225}
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