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Simplifying (5x + -15)(5x + -15) = 297 Reorder the terms: (-15 + 5x)(5x + -15) = 297 Reorder the terms: (-15 + 5x)(-15 + 5x) = 297 Multiply (-15 + 5x) * (-15 + 5x) (-15(-15 + 5x) + 5x * (-15 + 5x)) = 297 ((-15 * -15 + 5x * -15) + 5x * (-15 + 5x)) = 297 ((225 + -75x) + 5x * (-15 + 5x)) = 297 (225 + -75x + (-15 * 5x + 5x * 5x)) = 297 (225 + -75x + (-75x + 25x2)) = 297 Combine like terms: -75x + -75x = -150x (225 + -150x + 25x2) = 297 Solving 225 + -150x + 25x2 = 297 Solving for variable 'x'. Reorder the terms: 225 + -297 + -150x + 25x2 = 297 + -297 Combine like terms: 225 + -297 = -72 -72 + -150x + 25x2 = 297 + -297 Combine like terms: 297 + -297 = 0 -72 + -150x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.88 + -6x + x2 = 0 Move the constant term to the right: Add '2.88' to each side of the equation. -2.88 + -6x + 2.88 + x2 = 0 + 2.88 Reorder the terms: -2.88 + 2.88 + -6x + x2 = 0 + 2.88 Combine like terms: -2.88 + 2.88 = 0.00 0.00 + -6x + x2 = 0 + 2.88 -6x + x2 = 0 + 2.88 Combine like terms: 0 + 2.88 = 2.88 -6x + x2 = 2.88 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2.88 + 9 Reorder the terms: 9 + -6x + x2 = 2.88 + 9 Combine like terms: 2.88 + 9 = 11.88 9 + -6x + x2 = 11.88 Factor a perfect square on the left side: (x + -3)(x + -3) = 11.88 Calculate the square root of the right side: 3.446737588 Break this problem into two subproblems by setting (x + -3) equal to 3.446737588 and -3.446737588.Subproblem 1
x + -3 = 3.446737588 Simplifying x + -3 = 3.446737588 Reorder the terms: -3 + x = 3.446737588 Solving -3 + x = 3.446737588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.446737588 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.446737588 + 3 x = 3.446737588 + 3 Combine like terms: 3.446737588 + 3 = 6.446737588 x = 6.446737588 Simplifying x = 6.446737588Subproblem 2
x + -3 = -3.446737588 Simplifying x + -3 = -3.446737588 Reorder the terms: -3 + x = -3.446737588 Solving -3 + x = -3.446737588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.446737588 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.446737588 + 3 x = -3.446737588 + 3 Combine like terms: -3.446737588 + 3 = -0.446737588 x = -0.446737588 Simplifying x = -0.446737588Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.446737588, -0.446737588}
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