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Simplifying 51 = x(10 + 0.19x) 51 = (10 * x + 0.19x * x) 51 = (10x + 0.19x2) Solving 51 = 10x + 0.19x2 Solving for variable 'x'. Reorder the terms: 51 + -10x + -0.19x2 = 10x + -10x + 0.19x2 + -0.19x2 Combine like terms: 10x + -10x = 0 51 + -10x + -0.19x2 = 0 + 0.19x2 + -0.19x2 51 + -10x + -0.19x2 = 0.19x2 + -0.19x2 Combine like terms: 0.19x2 + -0.19x2 = 0.00 51 + -10x + -0.19x2 = 0.00 Begin completing the square. Divide all terms by -0.19 the coefficient of the squared term: Divide each side by '-0.19'. -268.4210526 + 52.63157895x + x2 = 0 Move the constant term to the right: Add '268.4210526' to each side of the equation. -268.4210526 + 52.63157895x + 268.4210526 + x2 = 0 + 268.4210526 Reorder the terms: -268.4210526 + 268.4210526 + 52.63157895x + x2 = 0 + 268.4210526 Combine like terms: -268.4210526 + 268.4210526 = 0.0000000 0.0000000 + 52.63157895x + x2 = 0 + 268.4210526 52.63157895x + x2 = 0 + 268.4210526 Combine like terms: 0 + 268.4210526 = 268.4210526 52.63157895x + x2 = 268.4210526 The x term is 52.63157895x. Take half its coefficient (26.31578948). Square it (692.5207760) and add it to both sides. Add '692.5207760' to each side of the equation. 52.63157895x + 692.5207760 + x2 = 268.4210526 + 692.5207760 Reorder the terms: 692.5207760 + 52.63157895x + x2 = 268.4210526 + 692.5207760 Combine like terms: 268.4210526 + 692.5207760 = 960.9418286 692.5207760 + 52.63157895x + x2 = 960.9418286 Factor a perfect square on the left side: (x + 26.31578948)(x + 26.31578948) = 960.9418286 Calculate the square root of the right side: 30.999061737 Break this problem into two subproblems by setting (x + 26.31578948) equal to 30.999061737 and -30.999061737.Subproblem 1
x + 26.31578948 = 30.999061737 Simplifying x + 26.31578948 = 30.999061737 Reorder the terms: 26.31578948 + x = 30.999061737 Solving 26.31578948 + x = 30.999061737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.31578948' to each side of the equation. 26.31578948 + -26.31578948 + x = 30.999061737 + -26.31578948 Combine like terms: 26.31578948 + -26.31578948 = 0.00000000 0.00000000 + x = 30.999061737 + -26.31578948 x = 30.999061737 + -26.31578948 Combine like terms: 30.999061737 + -26.31578948 = 4.683272257 x = 4.683272257 Simplifying x = 4.683272257Subproblem 2
x + 26.31578948 = -30.999061737 Simplifying x + 26.31578948 = -30.999061737 Reorder the terms: 26.31578948 + x = -30.999061737 Solving 26.31578948 + x = -30.999061737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.31578948' to each side of the equation. 26.31578948 + -26.31578948 + x = -30.999061737 + -26.31578948 Combine like terms: 26.31578948 + -26.31578948 = 0.00000000 0.00000000 + x = -30.999061737 + -26.31578948 x = -30.999061737 + -26.31578948 Combine like terms: -30.999061737 + -26.31578948 = -57.314851217 x = -57.314851217 Simplifying x = -57.314851217Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.683272257, -57.314851217}
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