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Simplifying -5(-6 + x2) = x (-6 * -5 + x2 * -5) = x (30 + -5x2) = x Solving 30 + -5x2 = x Solving for variable 'x'. Reorder the terms: 30 + -1x + -5x2 = x + -1x Combine like terms: x + -1x = 0 30 + -1x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6 + 0.2x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.2x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.2x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.2x + x2 = 0 + 6 0.2x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.2x + x2 = 6 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 6 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 6 + 0.01 Combine like terms: 6 + 0.01 = 6.01 0.01 + 0.2x + x2 = 6.01 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 6.01 Calculate the square root of the right side: 2.451530134 Break this problem into two subproblems by setting (x + 0.1) equal to 2.451530134 and -2.451530134.Subproblem 1
x + 0.1 = 2.451530134 Simplifying x + 0.1 = 2.451530134 Reorder the terms: 0.1 + x = 2.451530134 Solving 0.1 + x = 2.451530134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.451530134 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.451530134 + -0.1 x = 2.451530134 + -0.1 Combine like terms: 2.451530134 + -0.1 = 2.351530134 x = 2.351530134 Simplifying x = 2.351530134Subproblem 2
x + 0.1 = -2.451530134 Simplifying x + 0.1 = -2.451530134 Reorder the terms: 0.1 + x = -2.451530134 Solving 0.1 + x = -2.451530134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.451530134 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.451530134 + -0.1 x = -2.451530134 + -0.1 Combine like terms: -2.451530134 + -0.1 = -2.551530134 x = -2.551530134 Simplifying x = -2.551530134Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.351530134, -2.551530134}
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