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Simplifying 3x2 + -45x = -10 Reorder the terms: -45x + 3x2 = -10 Solving -45x + 3x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + -45x + 3x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -45x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -15x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -15x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -15x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -15x + x2 = 0 + -3.333333333 -15x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -15x + x2 = -3.333333333 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -3.333333333 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -3.333333333 + 56.25 Combine like terms: -3.333333333 + 56.25 = 52.916666667 56.25 + -15x + x2 = 52.916666667 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 52.916666667 Calculate the square root of the right side: 7.274384281 Break this problem into two subproblems by setting (x + -7.5) equal to 7.274384281 and -7.274384281.Subproblem 1
x + -7.5 = 7.274384281 Simplifying x + -7.5 = 7.274384281 Reorder the terms: -7.5 + x = 7.274384281 Solving -7.5 + x = 7.274384281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.274384281 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.274384281 + 7.5 x = 7.274384281 + 7.5 Combine like terms: 7.274384281 + 7.5 = 14.774384281 x = 14.774384281 Simplifying x = 14.774384281Subproblem 2
x + -7.5 = -7.274384281 Simplifying x + -7.5 = -7.274384281 Reorder the terms: -7.5 + x = -7.274384281 Solving -7.5 + x = -7.274384281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.274384281 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.274384281 + 7.5 x = -7.274384281 + 7.5 Combine like terms: -7.274384281 + 7.5 = 0.225615719 x = 0.225615719 Simplifying x = 0.225615719Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.774384281, 0.225615719}
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