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Simplifying 10x2 + -48x + 55 = 0 Reorder the terms: 55 + -48x + 10x2 = 0 Solving 55 + -48x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 5.5 + -4.8x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -4.8x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -4.8x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -4.8x + x2 = 0 + -5.5 -4.8x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -4.8x + x2 = -5.5 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = -5.5 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -5.5 + 5.76 Combine like terms: -5.5 + 5.76 = 0.26 5.76 + -4.8x + x2 = 0.26 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 0.26 Calculate the square root of the right side: 0.509901951 Break this problem into two subproblems by setting (x + -2.4) equal to 0.509901951 and -0.509901951.Subproblem 1
x + -2.4 = 0.509901951 Simplifying x + -2.4 = 0.509901951 Reorder the terms: -2.4 + x = 0.509901951 Solving -2.4 + x = 0.509901951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 0.509901951 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 0.509901951 + 2.4 x = 0.509901951 + 2.4 Combine like terms: 0.509901951 + 2.4 = 2.909901951 x = 2.909901951 Simplifying x = 2.909901951Subproblem 2
x + -2.4 = -0.509901951 Simplifying x + -2.4 = -0.509901951 Reorder the terms: -2.4 + x = -0.509901951 Solving -2.4 + x = -0.509901951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -0.509901951 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -0.509901951 + 2.4 x = -0.509901951 + 2.4 Combine like terms: -0.509901951 + 2.4 = 1.890098049 x = 1.890098049 Simplifying x = 1.890098049Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.909901951, 1.890098049}
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