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Simplifying 75x2 + -60x = -2 Reorder the terms: -60x + 75x2 = -2 Solving -60x + 75x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -60x + 75x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -60x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.02666666667 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.02666666667' to each side of the equation. 0.02666666667 + -0.8x + -0.02666666667 + x2 = 0 + -0.02666666667 Reorder the terms: 0.02666666667 + -0.02666666667 + -0.8x + x2 = 0 + -0.02666666667 Combine like terms: 0.02666666667 + -0.02666666667 = 0.00000000000 0.00000000000 + -0.8x + x2 = 0 + -0.02666666667 -0.8x + x2 = 0 + -0.02666666667 Combine like terms: 0 + -0.02666666667 = -0.02666666667 -0.8x + x2 = -0.02666666667 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.02666666667 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.02666666667 + 0.16 Combine like terms: -0.02666666667 + 0.16 = 0.13333333333 0.16 + -0.8x + x2 = 0.13333333333 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.13333333333 Calculate the square root of the right side: 0.365148372 Break this problem into two subproblems by setting (x + -0.4) equal to 0.365148372 and -0.365148372.Subproblem 1
x + -0.4 = 0.365148372 Simplifying x + -0.4 = 0.365148372 Reorder the terms: -0.4 + x = 0.365148372 Solving -0.4 + x = 0.365148372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.365148372 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.365148372 + 0.4 x = 0.365148372 + 0.4 Combine like terms: 0.365148372 + 0.4 = 0.765148372 x = 0.765148372 Simplifying x = 0.765148372Subproblem 2
x + -0.4 = -0.365148372 Simplifying x + -0.4 = -0.365148372 Reorder the terms: -0.4 + x = -0.365148372 Solving -0.4 + x = -0.365148372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.365148372 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.365148372 + 0.4 x = -0.365148372 + 0.4 Combine like terms: -0.365148372 + 0.4 = 0.034851628 x = 0.034851628 Simplifying x = 0.034851628Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.765148372, 0.034851628}
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