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Simplifying 5x2 + -15x + 4 = 0 Reorder the terms: 4 + -15x + 5x2 = 0 Solving 4 + -15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -3x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -3x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -3x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -3x + x2 = 0 + -0.8 -3x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -3x + x2 = -0.8 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.8 + 2.25 Combine like terms: -0.8 + 2.25 = 1.45 2.25 + -3x + x2 = 1.45 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x + -1.5) equal to 1.204159458 and -1.204159458.Subproblem 1
x + -1.5 = 1.204159458 Simplifying x + -1.5 = 1.204159458 Reorder the terms: -1.5 + x = 1.204159458 Solving -1.5 + x = 1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.204159458 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.204159458 + 1.5 x = 1.204159458 + 1.5 Combine like terms: 1.204159458 + 1.5 = 2.704159458 x = 2.704159458 Simplifying x = 2.704159458Subproblem 2
x + -1.5 = -1.204159458 Simplifying x + -1.5 = -1.204159458 Reorder the terms: -1.5 + x = -1.204159458 Solving -1.5 + x = -1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.204159458 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.204159458 + 1.5 x = -1.204159458 + 1.5 Combine like terms: -1.204159458 + 1.5 = 0.295840542 x = 0.295840542 Simplifying x = 0.295840542Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.704159458, 0.295840542}
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