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Simplifying 280x + 30 = 300x * 1.5x Reorder the terms: 30 + 280x = 300x * 1.5x Reorder the terms for easier multiplication: 30 + 280x = 300 * 1.5x * x Multiply 300 * 1.5 30 + 280x = 450x * x Multiply x * x 30 + 280x = 450x2 Solving 30 + 280x = 450x2 Solving for variable 'x'. Combine like terms: 450x2 + -450x2 = 0 30 + 280x + -450x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(3 + 28x + -45x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(3 + 28x + -45x2)' equal to zero and attempt to solve: Simplifying 3 + 28x + -45x2 = 0 Solving 3 + 28x + -45x2 = 0 Begin completing the square. Divide all terms by -45 the coefficient of the squared term: Divide each side by '-45'. -0.06666666667 + -0.6222222222x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + -0.6222222222x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + -0.6222222222x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + -0.6222222222x + x2 = 0 + 0.06666666667 -0.6222222222x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 -0.6222222222x + x2 = 0.06666666667 The x term is -0.6222222222x. Take half its coefficient (-0.3111111111). Square it (0.09679012345) and add it to both sides. Add '0.09679012345' to each side of the equation. -0.6222222222x + 0.09679012345 + x2 = 0.06666666667 + 0.09679012345 Reorder the terms: 0.09679012345 + -0.6222222222x + x2 = 0.06666666667 + 0.09679012345 Combine like terms: 0.06666666667 + 0.09679012345 = 0.16345679012 0.09679012345 + -0.6222222222x + x2 = 0.16345679012 Factor a perfect square on the left side: (x + -0.3111111111)(x + -0.3111111111) = 0.16345679012 Calculate the square root of the right side: 0.404297898 Break this problem into two subproblems by setting (x + -0.3111111111) equal to 0.404297898 and -0.404297898.Subproblem 1
x + -0.3111111111 = 0.404297898 Simplifying x + -0.3111111111 = 0.404297898 Reorder the terms: -0.3111111111 + x = 0.404297898 Solving -0.3111111111 + x = 0.404297898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3111111111' to each side of the equation. -0.3111111111 + 0.3111111111 + x = 0.404297898 + 0.3111111111 Combine like terms: -0.3111111111 + 0.3111111111 = 0.0000000000 0.0000000000 + x = 0.404297898 + 0.3111111111 x = 0.404297898 + 0.3111111111 Combine like terms: 0.404297898 + 0.3111111111 = 0.7154090091 x = 0.7154090091 Simplifying x = 0.7154090091Subproblem 2
x + -0.3111111111 = -0.404297898 Simplifying x + -0.3111111111 = -0.404297898 Reorder the terms: -0.3111111111 + x = -0.404297898 Solving -0.3111111111 + x = -0.404297898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3111111111' to each side of the equation. -0.3111111111 + 0.3111111111 + x = -0.404297898 + 0.3111111111 Combine like terms: -0.3111111111 + 0.3111111111 = 0.0000000000 0.0000000000 + x = -0.404297898 + 0.3111111111 x = -0.404297898 + 0.3111111111 Combine like terms: -0.404297898 + 0.3111111111 = -0.0931867869 x = -0.0931867869 Simplifying x = -0.0931867869Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7154090091, -0.0931867869}Solution
x = {0.7154090091, -0.0931867869}
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