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Simplifying 0.5x(x + 70) + 0.3x = 51 Reorder the terms: 0.5x(70 + x) + 0.3x = 51 (70 * 0.5x + x * 0.5x) + 0.3x = 51 (35x + 0.5x2) + 0.3x = 51 Reorder the terms: 35x + 0.3x + 0.5x2 = 51 Combine like terms: 35x + 0.3x = 35.3x 35.3x + 0.5x2 = 51 Solving 35.3x + 0.5x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + 35.3x + 0.5x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + 35.3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -102 + 70.6x + x2 = 0 Move the constant term to the right: Add '102' to each side of the equation. -102 + 70.6x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 70.6x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 70.6x + x2 = 0 + 102 70.6x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 70.6x + x2 = 102 The x term is 70.6x. Take half its coefficient (35.3). Square it (1246.09) and add it to both sides. Add '1246.09' to each side of the equation. 70.6x + 1246.09 + x2 = 102 + 1246.09 Reorder the terms: 1246.09 + 70.6x + x2 = 102 + 1246.09 Combine like terms: 102 + 1246.09 = 1348.09 1246.09 + 70.6x + x2 = 1348.09 Factor a perfect square on the left side: (x + 35.3)(x + 35.3) = 1348.09 Calculate the square root of the right side: 36.716345134 Break this problem into two subproblems by setting (x + 35.3) equal to 36.716345134 and -36.716345134.Subproblem 1
x + 35.3 = 36.716345134 Simplifying x + 35.3 = 36.716345134 Reorder the terms: 35.3 + x = 36.716345134 Solving 35.3 + x = 36.716345134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.3' to each side of the equation. 35.3 + -35.3 + x = 36.716345134 + -35.3 Combine like terms: 35.3 + -35.3 = 0.0 0.0 + x = 36.716345134 + -35.3 x = 36.716345134 + -35.3 Combine like terms: 36.716345134 + -35.3 = 1.416345134 x = 1.416345134 Simplifying x = 1.416345134Subproblem 2
x + 35.3 = -36.716345134 Simplifying x + 35.3 = -36.716345134 Reorder the terms: 35.3 + x = -36.716345134 Solving 35.3 + x = -36.716345134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.3' to each side of the equation. 35.3 + -35.3 + x = -36.716345134 + -35.3 Combine like terms: 35.3 + -35.3 = 0.0 0.0 + x = -36.716345134 + -35.3 x = -36.716345134 + -35.3 Combine like terms: -36.716345134 + -35.3 = -72.016345134 x = -72.016345134 Simplifying x = -72.016345134Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.416345134, -72.016345134}
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