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Simplifying 5x2 = 96x + 36 Reorder the terms: 5x2 = 36 + 96x Solving 5x2 = 36 + 96x Solving for variable 'x'. Reorder the terms: -36 + -96x + 5x2 = 36 + 96x + -36 + -96x Reorder the terms: -36 + -96x + 5x2 = 36 + -36 + 96x + -96x Combine like terms: 36 + -36 = 0 -36 + -96x + 5x2 = 0 + 96x + -96x -36 + -96x + 5x2 = 96x + -96x Combine like terms: 96x + -96x = 0 -36 + -96x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -19.2x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -19.2x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -19.2x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -19.2x + x2 = 0 + 7.2 -19.2x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -19.2x + x2 = 7.2 The x term is -19.2x. Take half its coefficient (-9.6). Square it (92.16) and add it to both sides. Add '92.16' to each side of the equation. -19.2x + 92.16 + x2 = 7.2 + 92.16 Reorder the terms: 92.16 + -19.2x + x2 = 7.2 + 92.16 Combine like terms: 7.2 + 92.16 = 99.36 92.16 + -19.2x + x2 = 99.36 Factor a perfect square on the left side: (x + -9.6)(x + -9.6) = 99.36 Calculate the square root of the right side: 9.967948636 Break this problem into two subproblems by setting (x + -9.6) equal to 9.967948636 and -9.967948636.Subproblem 1
x + -9.6 = 9.967948636 Simplifying x + -9.6 = 9.967948636 Reorder the terms: -9.6 + x = 9.967948636 Solving -9.6 + x = 9.967948636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.6' to each side of the equation. -9.6 + 9.6 + x = 9.967948636 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = 9.967948636 + 9.6 x = 9.967948636 + 9.6 Combine like terms: 9.967948636 + 9.6 = 19.567948636 x = 19.567948636 Simplifying x = 19.567948636Subproblem 2
x + -9.6 = -9.967948636 Simplifying x + -9.6 = -9.967948636 Reorder the terms: -9.6 + x = -9.967948636 Solving -9.6 + x = -9.967948636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.6' to each side of the equation. -9.6 + 9.6 + x = -9.967948636 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = -9.967948636 + 9.6 x = -9.967948636 + 9.6 Combine like terms: -9.967948636 + 9.6 = -0.367948636 x = -0.367948636 Simplifying x = -0.367948636Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.567948636, -0.367948636}
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