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Simplifying 25x2 + 3x = 12 Reorder the terms: 3x + 25x2 = 12 Solving 3x + 25x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 3x + 25x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 3x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + 0.12x + x2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + 0.12x + 0.48 + x2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + 0.12x + x2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + 0.12x + x2 = 0 + 0.48 0.12x + x2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 0.12x + x2 = 0.48 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 0.48 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 0.48 + 0.0036 Combine like terms: 0.48 + 0.0036 = 0.4836 0.0036 + 0.12x + x2 = 0.4836 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 0.4836 Calculate the square root of the right side: 0.695413546 Break this problem into two subproblems by setting (x + 0.06) equal to 0.695413546 and -0.695413546.Subproblem 1
x + 0.06 = 0.695413546 Simplifying x + 0.06 = 0.695413546 Reorder the terms: 0.06 + x = 0.695413546 Solving 0.06 + x = 0.695413546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 0.695413546 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.695413546 + -0.06 x = 0.695413546 + -0.06 Combine like terms: 0.695413546 + -0.06 = 0.635413546 x = 0.635413546 Simplifying x = 0.635413546Subproblem 2
x + 0.06 = -0.695413546 Simplifying x + 0.06 = -0.695413546 Reorder the terms: 0.06 + x = -0.695413546 Solving 0.06 + x = -0.695413546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -0.695413546 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.695413546 + -0.06 x = -0.695413546 + -0.06 Combine like terms: -0.695413546 + -0.06 = -0.755413546 x = -0.755413546 Simplifying x = -0.755413546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.635413546, -0.755413546}
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