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Simplifying 3x(x + -5) = 7 Reorder the terms: 3x(-5 + x) = 7 (-5 * 3x + x * 3x) = 7 (-15x + 3x2) = 7 Solving -15x + 3x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -15x + 3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -5x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -5x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -5x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + 2.333333333 -5x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -5x + x2 = 2.333333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2.333333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.333333333 + 6.25 Combine like terms: 2.333333333 + 6.25 = 8.583333333 6.25 + -5x + x2 = 8.583333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.583333333 Calculate the square root of the right side: 2.929732638 Break this problem into two subproblems by setting (x + -2.5) equal to 2.929732638 and -2.929732638.Subproblem 1
x + -2.5 = 2.929732638 Simplifying x + -2.5 = 2.929732638 Reorder the terms: -2.5 + x = 2.929732638 Solving -2.5 + x = 2.929732638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.929732638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.929732638 + 2.5 x = 2.929732638 + 2.5 Combine like terms: 2.929732638 + 2.5 = 5.429732638 x = 5.429732638 Simplifying x = 5.429732638Subproblem 2
x + -2.5 = -2.929732638 Simplifying x + -2.5 = -2.929732638 Reorder the terms: -2.5 + x = -2.929732638 Solving -2.5 + x = -2.929732638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.929732638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.929732638 + 2.5 x = -2.929732638 + 2.5 Combine like terms: -2.929732638 + 2.5 = -0.429732638 x = -0.429732638 Simplifying x = -0.429732638Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.429732638, -0.429732638}
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