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Simplifying x(5x + -14) = 84(25) Reorder the terms: x(-14 + 5x) = 84(25) (-14 * x + 5x * x) = 84(25) (-14x + 5x2) = 84(25) Multiply 84 * 25 -14x + 5x2 = 2100 Solving -14x + 5x2 = 2100 Solving for variable 'x'. Reorder the terms: -2100 + -14x + 5x2 = 2100 + -2100 Combine like terms: 2100 + -2100 = 0 -2100 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -420 + -2.8x + x2 = 0 Move the constant term to the right: Add '420' to each side of the equation. -420 + -2.8x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + -2.8x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + -2.8x + x2 = 0 + 420 -2.8x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 -2.8x + x2 = 420 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 420 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 420 + 1.96 Combine like terms: 420 + 1.96 = 421.96 1.96 + -2.8x + x2 = 421.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 421.96 Calculate the square root of the right side: 20.541664976 Break this problem into two subproblems by setting (x + -1.4) equal to 20.541664976 and -20.541664976.Subproblem 1
x + -1.4 = 20.541664976 Simplifying x + -1.4 = 20.541664976 Reorder the terms: -1.4 + x = 20.541664976 Solving -1.4 + x = 20.541664976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 20.541664976 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 20.541664976 + 1.4 x = 20.541664976 + 1.4 Combine like terms: 20.541664976 + 1.4 = 21.941664976 x = 21.941664976 Simplifying x = 21.941664976Subproblem 2
x + -1.4 = -20.541664976 Simplifying x + -1.4 = -20.541664976 Reorder the terms: -1.4 + x = -20.541664976 Solving -1.4 + x = -20.541664976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -20.541664976 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -20.541664976 + 1.4 x = -20.541664976 + 1.4 Combine like terms: -20.541664976 + 1.4 = -19.141664976 x = -19.141664976 Simplifying x = -19.141664976Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.941664976, -19.141664976}
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