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Simplifying 1440 = 3x + 5x(410 + -1x) 1440 = 3x + (410 * 5x + -1x * 5x) 1440 = 3x + (2050x + -5x2) Combine like terms: 3x + 2050x = 2053x 1440 = 2053x + -5x2 Solving 1440 = 2053x + -5x2 Solving for variable 'x'. Reorder the terms: 1440 + -2053x + 5x2 = 2053x + -2053x + -5x2 + 5x2 Combine like terms: 2053x + -2053x = 0 1440 + -2053x + 5x2 = 0 + -5x2 + 5x2 1440 + -2053x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 1440 + -2053x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 288 + -410.6x + x2 = 0 Move the constant term to the right: Add '-288' to each side of the equation. 288 + -410.6x + -288 + x2 = 0 + -288 Reorder the terms: 288 + -288 + -410.6x + x2 = 0 + -288 Combine like terms: 288 + -288 = 0 0 + -410.6x + x2 = 0 + -288 -410.6x + x2 = 0 + -288 Combine like terms: 0 + -288 = -288 -410.6x + x2 = -288 The x term is -410.6x. Take half its coefficient (-205.3). Square it (42148.09) and add it to both sides. Add '42148.09' to each side of the equation. -410.6x + 42148.09 + x2 = -288 + 42148.09 Reorder the terms: 42148.09 + -410.6x + x2 = -288 + 42148.09 Combine like terms: -288 + 42148.09 = 41860.09 42148.09 + -410.6x + x2 = 41860.09 Factor a perfect square on the left side: (x + -205.3)(x + -205.3) = 41860.09 Calculate the square root of the right side: 204.597385125 Break this problem into two subproblems by setting (x + -205.3) equal to 204.597385125 and -204.597385125.Subproblem 1
x + -205.3 = 204.597385125 Simplifying x + -205.3 = 204.597385125 Reorder the terms: -205.3 + x = 204.597385125 Solving -205.3 + x = 204.597385125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '205.3' to each side of the equation. -205.3 + 205.3 + x = 204.597385125 + 205.3 Combine like terms: -205.3 + 205.3 = 0.0 0.0 + x = 204.597385125 + 205.3 x = 204.597385125 + 205.3 Combine like terms: 204.597385125 + 205.3 = 409.897385125 x = 409.897385125 Simplifying x = 409.897385125Subproblem 2
x + -205.3 = -204.597385125 Simplifying x + -205.3 = -204.597385125 Reorder the terms: -205.3 + x = -204.597385125 Solving -205.3 + x = -204.597385125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '205.3' to each side of the equation. -205.3 + 205.3 + x = -204.597385125 + 205.3 Combine like terms: -205.3 + 205.3 = 0.0 0.0 + x = -204.597385125 + 205.3 x = -204.597385125 + 205.3 Combine like terms: -204.597385125 + 205.3 = 0.702614875 x = 0.702614875 Simplifying x = 0.702614875Solution
The solution to the problem is based on the solutions from the subproblems. x = {409.897385125, 0.702614875}
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