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Simplifying (0.2x + -3)(0.2x + -3) = 0 Reorder the terms: (-3 + 0.2x)(0.2x + -3) = 0 Reorder the terms: (-3 + 0.2x)(-3 + 0.2x) = 0 Multiply (-3 + 0.2x) * (-3 + 0.2x) (-3(-3 + 0.2x) + 0.2x * (-3 + 0.2x)) = 0 ((-3 * -3 + 0.2x * -3) + 0.2x * (-3 + 0.2x)) = 0 ((9 + -0.6x) + 0.2x * (-3 + 0.2x)) = 0 (9 + -0.6x + (-3 * 0.2x + 0.2x * 0.2x)) = 0 (9 + -0.6x + (-0.6x + 0.04x2)) = 0 Combine like terms: -0.6x + -0.6x = -1.2x (9 + -1.2x + 0.04x2) = 0 Solving 9 + -1.2x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 225 + -30x + x2 = 0 Move the constant term to the right: Add '-225' to each side of the equation. 225 + -30x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -30x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -30x + x2 = 0 + -225 -30x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -30x + x2 = -225 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -225 + 225 Reorder the terms: 225 + -30x + x2 = -225 + 225 Combine like terms: -225 + 225 = 0 225 + -30x + x2 = 0 Factor a perfect square on the left side: (x + -15)(x + -15) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -15) equal to 0 and 0.Subproblem 1
x + -15 = 0 Simplifying x + -15 = 0 Reorder the terms: -15 + x = 0 Solving -15 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x = 0 + 15 x = 0 + 15 Combine like terms: 0 + 15 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -15 = 0 Simplifying x + -15 = 0 Reorder the terms: -15 + x = 0 Solving -15 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x = 0 + 15 x = 0 + 15 Combine like terms: 0 + 15 = 15 x = 15 Simplifying x = 15Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, 15}
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