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Simplifying x2 + -30x + 70 = 0 Reorder the terms: 70 + -30x + x2 = 0 Solving 70 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -30x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -30x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -30x + x2 = 0 + -70 -30x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -30x + x2 = -70 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -70 + 225 Reorder the terms: 225 + -30x + x2 = -70 + 225 Combine like terms: -70 + 225 = 155 225 + -30x + x2 = 155 Factor a perfect square on the left side: (x + -15)(x + -15) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (x + -15) equal to 12.449899598 and -12.449899598.Subproblem 1
x + -15 = 12.449899598 Simplifying x + -15 = 12.449899598 Reorder the terms: -15 + x = 12.449899598 Solving -15 + x = 12.449899598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 12.449899598 + 15 Combine like terms: -15 + 15 = 0 0 + x = 12.449899598 + 15 x = 12.449899598 + 15 Combine like terms: 12.449899598 + 15 = 27.449899598 x = 27.449899598 Simplifying x = 27.449899598Subproblem 2
x + -15 = -12.449899598 Simplifying x + -15 = -12.449899598 Reorder the terms: -15 + x = -12.449899598 Solving -15 + x = -12.449899598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -12.449899598 + 15 Combine like terms: -15 + 15 = 0 0 + x = -12.449899598 + 15 x = -12.449899598 + 15 Combine like terms: -12.449899598 + 15 = 2.550100402 x = 2.550100402 Simplifying x = 2.550100402Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.449899598, 2.550100402}
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