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Simplifying 5x(14 + -1x) = -30 + -2x (14 * 5x + -1x * 5x) = -30 + -2x (70x + -5x2) = -30 + -2x Solving 70x + -5x2 = -30 + -2x Solving for variable 'x'. Reorder the terms: 30 + 70x + 2x + -5x2 = -30 + -2x + 30 + 2x Combine like terms: 70x + 2x = 72x 30 + 72x + -5x2 = -30 + -2x + 30 + 2x Reorder the terms: 30 + 72x + -5x2 = -30 + 30 + -2x + 2x Combine like terms: -30 + 30 = 0 30 + 72x + -5x2 = 0 + -2x + 2x 30 + 72x + -5x2 = -2x + 2x Combine like terms: -2x + 2x = 0 30 + 72x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6 + -14.4x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -14.4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -14.4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -14.4x + x2 = 0 + 6 -14.4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -14.4x + x2 = 6 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = 6 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = 6 + 51.84 Combine like terms: 6 + 51.84 = 57.84 51.84 + -14.4x + x2 = 57.84 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 57.84 Calculate the square root of the right side: 7.605261337 Break this problem into two subproblems by setting (x + -7.2) equal to 7.605261337 and -7.605261337.Subproblem 1
x + -7.2 = 7.605261337 Simplifying x + -7.2 = 7.605261337 Reorder the terms: -7.2 + x = 7.605261337 Solving -7.2 + x = 7.605261337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = 7.605261337 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 7.605261337 + 7.2 x = 7.605261337 + 7.2 Combine like terms: 7.605261337 + 7.2 = 14.805261337 x = 14.805261337 Simplifying x = 14.805261337Subproblem 2
x + -7.2 = -7.605261337 Simplifying x + -7.2 = -7.605261337 Reorder the terms: -7.2 + x = -7.605261337 Solving -7.2 + x = -7.605261337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = -7.605261337 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -7.605261337 + 7.2 x = -7.605261337 + 7.2 Combine like terms: -7.605261337 + 7.2 = -0.405261337 x = -0.405261337 Simplifying x = -0.405261337Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.805261337, -0.405261337}
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