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Simplifying 5x2 + 3 = 12x Reorder the terms: 3 + 5x2 = 12x Solving 3 + 5x2 = 12x Solving for variable 'x'. Reorder the terms: 3 + -12x + 5x2 = 12x + -12x Combine like terms: 12x + -12x = 0 3 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.4x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.4x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.4x + x2 = 0 + -0.6 -2.4x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.4x + x2 = -0.6 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.6 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.6 + 1.44 Combine like terms: -0.6 + 1.44 = 0.84 1.44 + -2.4x + x2 = 0.84 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + -1.2) equal to 0.916515139 and -0.916515139.Subproblem 1
x + -1.2 = 0.916515139 Simplifying x + -1.2 = 0.916515139 Reorder the terms: -1.2 + x = 0.916515139 Solving -1.2 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.916515139 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.916515139 + 1.2 x = 0.916515139 + 1.2 Combine like terms: 0.916515139 + 1.2 = 2.116515139 x = 2.116515139 Simplifying x = 2.116515139Subproblem 2
x + -1.2 = -0.916515139 Simplifying x + -1.2 = -0.916515139 Reorder the terms: -1.2 + x = -0.916515139 Solving -1.2 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.916515139 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.916515139 + 1.2 x = -0.916515139 + 1.2 Combine like terms: -0.916515139 + 1.2 = 0.283484861 x = 0.283484861 Simplifying x = 0.283484861Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.116515139, 0.283484861}
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