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Simplifying 2x(10x + -3) = 24 Reorder the terms: 2x(-3 + 10x) = 24 (-3 * 2x + 10x * 2x) = 24 (-6x + 20x2) = 24 Solving -6x + 20x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -6x + 20x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -6x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -3x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -3x + 10x2)' equal to zero and attempt to solve: Simplifying -12 + -3x + 10x2 = 0 Solving -12 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.3x + 1.2 + x2 = 0.0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.3x + x2 = 0.0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.3x + x2 = 0.0 + 1.2 -0.3x + x2 = 0.0 + 1.2 Combine like terms: 0.0 + 1.2 = 1.2 -0.3x + x2 = 1.2 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 1.2 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 1.2 + 0.0225 Combine like terms: 1.2 + 0.0225 = 1.2225 0.0225 + -0.3x + x2 = 1.2225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 1.2225 Calculate the square root of the right side: 1.105667219 Break this problem into two subproblems by setting (x + -0.15) equal to 1.105667219 and -1.105667219.Subproblem 1
x + -0.15 = 1.105667219 Simplifying x + -0.15 = 1.105667219 Reorder the terms: -0.15 + x = 1.105667219 Solving -0.15 + x = 1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 1.105667219 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.105667219 + 0.15 x = 1.105667219 + 0.15 Combine like terms: 1.105667219 + 0.15 = 1.255667219 x = 1.255667219 Simplifying x = 1.255667219Subproblem 2
x + -0.15 = -1.105667219 Simplifying x + -0.15 = -1.105667219 Reorder the terms: -0.15 + x = -1.105667219 Solving -0.15 + x = -1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -1.105667219 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.105667219 + 0.15 x = -1.105667219 + 0.15 Combine like terms: -1.105667219 + 0.15 = -0.955667219 x = -0.955667219 Simplifying x = -0.955667219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.255667219, -0.955667219}Solution
x = {1.255667219, -0.955667219}
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