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Simplifying 3(x + 25) * x = 5 Reorder the terms: 3(25 + x) * x = 5 Reorder the terms for easier multiplication: 3x(25 + x) = 5 (25 * 3x + x * 3x) = 5 (75x + 3x2) = 5 Solving 75x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 75x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 75x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 25x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 25x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 25x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 25x + x2 = 0 + 1.666666667 25x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 25x + x2 = 1.666666667 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 1.666666667 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 1.666666667 + 156.25 Combine like terms: 1.666666667 + 156.25 = 157.916666667 156.25 + 25x + x2 = 157.916666667 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 157.916666667 Calculate the square root of the right side: 12.566489831 Break this problem into two subproblems by setting (x + 12.5) equal to 12.566489831 and -12.566489831.Subproblem 1
x + 12.5 = 12.566489831 Simplifying x + 12.5 = 12.566489831 Reorder the terms: 12.5 + x = 12.566489831 Solving 12.5 + x = 12.566489831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.566489831 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.566489831 + -12.5 x = 12.566489831 + -12.5 Combine like terms: 12.566489831 + -12.5 = 0.066489831 x = 0.066489831 Simplifying x = 0.066489831Subproblem 2
x + 12.5 = -12.566489831 Simplifying x + 12.5 = -12.566489831 Reorder the terms: 12.5 + x = -12.566489831 Solving 12.5 + x = -12.566489831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.566489831 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.566489831 + -12.5 x = -12.566489831 + -12.5 Combine like terms: -12.566489831 + -12.5 = -25.066489831 x = -25.066489831 Simplifying x = -25.066489831Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066489831, -25.066489831}
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